Patent Publication Number: US-2022223049-A1

Title: Methods and apparatus for observer-based landing control of a vehicle

Description:
RELATED APPLICATIONS 
     This patent claims the benefit of U.S. Provisional Patent Application No. 63/135,251, which was filed on Jan. 8, 2021. U.S. Provisional Patent Application No. 63/135,251 is hereby incorporated herein by reference in its entirety. Priority to U.S. Provisional Patent Application No. 63/135,251 is hereby claimed. 
     This patent includes subject matter related to U.S. Pat. No. 10,216,198 and U.S. Pat. No. 10,852,748, all of which are hereby incorporated by reference in their entireties. 
    
    
     FIELD OF THE DISCLOSURE 
     This disclosure relates generally to vehicles and, more particularly, to methods and apparatus to perform observer-based landing control of a vehicle. 
     BACKGROUND 
     In recent years, vehicle control systems, like those used in aircraft, automotive, and marine vehicles, have grown progressively more complex with the proliferation of newer and more powerful controllers. Some vehicle control systems include one or more controllers capable of implementing a greater number of complex algorithms for measuring and/or controlling different aspects of a vehicle. Control systems continue to incorporate applications of advanced control theory that previously were not feasible to implement due to software and/or hardware limitations. In addition, the applications of the control theory continue to be modified for adaptation on newer processor architectures. 
     Some vehicle control systems include implementations of control theory based on whether a state of the vehicle is known. In some examples, the state of the vehicle is known (measured), which enables the vehicle control system to generate a control command based on a known state of the vehicle. However, in some instances, the state of the vehicle is partially known or completely unknown. In this case, only output measurements from the vehicle sensors (such as inertial measurement units (IMUS) and rate gyros) are available to synthesize a control policy. An unknown state of the vehicle presents additional challenges to the vehicle control system such as, for example, generating a control command based on an estimation of the state of the vehicle. The estimation of the state of the vehicle requires additional processing power to perform complex algorithmic calculations based on advanced control theory techniques. Algorithms that rely on estimation of the vehicle state based on a suite of sensors are referred to as “observer-based control.” 
     SUMMARY 
     An example apparatus disclosed herein includes at least one memory, and at least one processor to execute instructions to at least in response to determining an aircraft is in a flare regime of a flight plan, determine an estimate state of an aircraft parameter based on an execution of a transfer function of an observer model, the execution of the transfer function based on an altitude command corresponding to the flare regime, determine a gain value based on a measured state of the aircraft parameter, determine an altitude control input based on the estimate state and the gain value, determine an altitude command output based on the altitude control input and longitudinal dynamics of the aircraft, the longitudinal dynamics generated in response to the aircraft executing the altitude command output, and control an elevator of the aircraft based on the altitude command output. 
     An example tangible computer-readable storage medium disclosed herein includes instructions that, when executed, cause at least one processor to at least in response to determining an aircraft is in a flare regime of a flight plan, determine an estimate state of an aircraft parameter based on an execution of a transfer function of an observer model, the execution of the transfer function based on an altitude command corresponding to the flare regime, determine a gain value based on a measured state of the aircraft parameter, determine an altitude control input based on the estimate state and the gain value, determine an altitude command output based on the altitude control input and longitudinal dynamics of the aircraft, the longitudinal dynamics generated in response to the aircraft executing the altitude command output, and control an elevator of the aircraft based on the altitude command output. 
     An example method disclosed herein includes in response to determining an aircraft is in a flare regime of a flight plan, determining an estimate state of an aircraft parameter based on an execution of a transfer function of an observer model, the execution of the transfer function based on an altitude command, determining a gain value based on an aircraft parameter, determining an altitude control input based on the estimate state and the gain value, determining an altitude command output based on the altitude control input and longitudinal dynamics of the aircraft, the longitudinal dynamics generated in response to the aircraft executing the altitude command output, and controlling an elevator of the aircraft based on the altitude command output. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an illustration of an example aircraft that includes an example vehicle controller to implement observer-based landing control of the aircraft. 
         FIG. 2  is an illustration of the example aircraft of  FIG. 1  operating in an example flare regime of an example flight plan. 
         FIG. 3  is a block diagram of a first example implementation of the example vehicle controller of  FIG. 1 . 
         FIG. 4  is a block diagram of a second example implementation of the example vehicle controller of  FIG. 1 . 
         FIG. 5  is a block diagram of a third example implementation of the example vehicle controller of  FIG. 1 . 
         FIG. 6  is a flowchart representative of example machine readable instructions that may be executed to implement the example vehicle controller of  FIGS. 1, 3, 4 , and/or  5  to facilitate observer-based landing control of the example aircraft of  FIGS. 1 and/or 2 . 
         FIG. 7  is another flowchart representative of example machine readable instructions that may be executed to implement the example vehicle controller of  FIGS. 1, 3, 4 , and/or  5  to facilitate observer-based landing control of the example aircraft of  FIGS. 1  and/or 2. 
         FIG. 8  is yet another flowchart representative of example machine readable instructions that may be executed to implement the example vehicle controller of  FIGS. 1, 3, 4 , and/or  5  to facilitate observer-based landing control of the example aircraft of  FIGS. 1 and/or 2 . 
         FIG. 9  is a flowchart representative of example machine readable instructions that may be executed to implement the example vehicle controller of  FIGS. 1, 3, 4 , and/or  5  to determine example input(s) to an example observer transfer function based on an example altitude command and example measured states. 
         FIG. 10  is a block diagram of an example processing platform structured to execute the example machine-readable instructions of  FIGS. 6-9  to implement the example vehicle controller of  FIGS. 1, 3, 4 , and/or  5 . 
         FIG. 11  is a block diagram of an example software distribution platform to distribute software (e.g., software corresponding to the example computer readable instructions of  FIGS. 6-9 ) to example devices such as original equipment manufacturers (OEMs) (e.g., for inclusion in products to be distributed to, for example, aircraft manufacturers and/or to direct buy aircraft customers). 
     
    
    
     DETAILED DESCRIPTION 
     The figures are not to scale. In general, the same reference numbers will be used throughout the drawing(s) and accompanying written description to refer to the same or like parts. As used herein, connection references (e.g., attached, coupled, connected, and joined) may include intermediate members between the elements referenced by the connection reference and/or relative movement between those elements unless otherwise indicated. As such, connection references do not necessarily infer that two elements are directly connected and/or in fixed relation to each other. As used herein, stating that any part is in “contact” with another part is defined to mean that there is no intermediate part between the two parts. 
     Unless specifically stated otherwise, descriptors such as “first,” “second,” “third,” etc., are used herein without imputing or otherwise indicating any meaning of priority, physical order, arrangement in a list, and/or ordering in any way, but are merely used as labels and/or arbitrary names to distinguish elements for ease of understanding the disclosed examples. In some examples, the descriptor “first” may be used to refer to an element in the detailed description, while the same element may be referred to in a claim with a different descriptor such as “second” or “third.” In such instances, it should be understood that such descriptors are used merely for identifying those elements distinctly that might, for example, otherwise share a same name. 
     Some vehicle manufacturers have invested in vehicle control system designs to improve accuracy and robustness. The vehicle control system designs may include implementations of control theory based on whether a state of a vehicle parameter is known. In some examples, the state of the vehicle parameter is known, which enables the vehicle control system to generate a control command based on a known state of the vehicle parameter. As used herein, the term “vehicle” may refer to an air-based vehicle (e.g., aircraft, an unmanned aerial vehicle (UAV), etc.), a land-based vehicle (e.g., an automobile, a bus, a train, etc.), and/or a water or marine-based vehicle (e.g., a boat, a submarine, etc.). In some examples, the vehicle parameter may be an aircraft parameter, such as an angle of attack, a pitch rate, a first flex mode position, a second flex mode position, a first flex mode velocity, a second flex mode velocity, etc. A state of the aircraft parameter may include a value based on a measurement from a sensor, a matrix of one or more values based on one or more measurements from one or more sensors, etc. For example, a state associated with an aircraft may be measured based on one or more sensors, such as one or more acceleration sensors (e.g., an accelerometer), one or more angle of attack sensors, one or more angular rate sensors (e.g., a gyro sensor), etc., and/or a combination thereof. 
     In some examples, the vehicle control systems that generate commands based on known states of vehicle parameters may utilize state-space representations to develop mathematical models of a physical system (e.g., an actuator, a vehicle, etc.). The state-space representation may include a set of input, output, and state variables related by first-order ordinary differential equations. For example, a representation of a continuous time-variant system that includes m inputs, p outputs, and n state variables may be described in accordance with Equation (1) and Equation (2) below: 
         x _dot( t )= A ( t ) x ( t )+ B ( t ) u ( t )   Equation (1)
 
         y ( t )= C ( t ) x ( t )+ D ( t ) u ( t )   Equation (2)
 
     In the illustrated example of Equation (1) above, the variable x_dot(t) represents the vehicle state derivative vector, the variable A(t) represents a state matrix or a system matrix, where a dimension of A(t) is denoted by dim[A(t)]=n×n, and the variable x(t) represents a state vector, where x(t) ∈ R n . The term R n  represents a Euclidean n-dimensional space. In the illustrated example of Equation (1) above, the variable B(t) represents an input matrix where a dimension of B(t) is denoted by dim[B(t)]=n×m, and the variable u(t) represents an input vector or a control vector, where u(t) ∈ R m . In the illustrated example of Equation (2) above, the variable y(t) represents an output vector, where y(t) ∈ R n , the variable C(t) represents an output matrix, where a dimension of C(t) is denoted by dim[C(t)]=p×n, and the variable x(t) represents the state vector, where x(t) ∈ R n . In the illustrated example of Equation (2) above, the variable D(t) represents a control-feedthrough matrix (i.e., a feedforward matrix) where a dimension of D(t) is denoted by dim[D(t)]=p×m, and the variable u(t) represents the input vector or the control vector, where u(t) ∈ R m . 
     In some examples, controllability is a property of the vehicle control system. The controllability of a system may denote an ability to move a system around the entire configuration space of the system using only specified admissible manipulations. An example variation of controllability is state controllability. State controllability may be a condition that implies a plausibility to move a state of a parameter and/or a state of a system from any initial value to any final value within a finite time window. For example, a continuous time-invariant linear state-space model may be controllable if and only if rank [B AB A 2 B . . . A n−1 B]=n, where rank is a number of linearly independent rows in a matrix, the variable n is a number of state variables, the variable A is the state matrix, and the variable B is the input matrix. 
     In some examples, observability may be another property of the vehicle control system. For example, the observability of a system may be a measure for how well one or more internal states of a system (e.g., an aircraft, a flight control surface of the aircraft, etc.) can be inferred by knowing one or more external outputs of the system. In some such examples, the controllability and the observability of the system are mathematical duals. For example, the controllability of the system may denote that an input can bring any initial state to any final state, whereas the observability may denote that knowing an output of the system provides sufficient information to predict an initial state of the system. 
     In some examples, the state of the vehicle is unknown. An unknown state of the vehicle may present additional challenges to some such vehicle control systems such as generating the control command based on an estimation of the state of the vehicle. The estimation of the state of the vehicle may require additional hardware resources (e.g., compute (e.g., one or more processors), memory (e.g., one or more memory devices), and/or storage (e.g., one more storage discs or storage devices) hardware resources) to perform complex algorithmic calculations based on advanced control theory techniques. For example, to compensate for the unknown state (e.g., no a priori information regarding the state is known), a controller may implement state observers. In some examples, the controller may also use adaptive control to generate one or more control laws to compensate for unknown parameters. 
     In some examples, the vehicle control system may utilize a state observer to determine an estimate of an unknown state of the vehicle and/or an unknown state of a parameter of the vehicle. The state observer may calculate the estimate of the unknown state based on a measurement from a suite of sensors. The state observer may obtain measurements related to an input and an output of the vehicle. For example, the state observer may obtain an initial command for an input to an aircraft control system (e.g., a guidance command). In such examples, the state observer may obtain an output measurement from the vehicle sensors (e.g., the accelerometers, the rate gyros, etc.). For example, a representation of an observer model for a continuous-time-variant linear system for the vehicle that includes m inputs, p outputs, and n state variables may be described in accordance with the examples of Equation (3) and Equation (4) below: 
         {dot over ({circumflex over (x)})} ( t )= A ( t ){circumflex over (x)}( t )+ B ( t ) u ( t )+ L ( y ( t )− ŷ ( t ))   Equation (3)
 
         ŷ ( t )= C ( t ) {circumflex over (x)} ( t )+ D ( t ) u ( t )   Equation (4)
 
     In the illustrated example of Equation (3) above, the variable {dot over ({circumflex over (x)})}(t) represents an estimate of the observer state derivative vector, the variable A(t) represents a state matrix or a system matrix, where a dimension of A(t) is denoted by dim[A(t)]=n×n, and the variable {circumflex over (x)}(t) represents an estimate of a state vector, where {circumflex over (x)}(t) ∈ R n . The term R n  represents a Euclidean n-dimensional space. In the illustrated example of Equation (3) above, the variable B(t) represents an input matrix, where a dimension of B(t) is denoted by dim[B(t)]=n×m, and the variable u(t) represents an input vector or a control vector, where u(t) ∈ R m . In the illustrated example of Equation (3) above, the variable L represents an observer error feedback gain, the variable y(t) represents the measurement or output vector, where y(t) ∈ R p , and the variable ŷ(t) represents an estimate of an output vector. The variable L may be represented and parameterized as L v , where v represents a small positive constant, which in turn represents the observer model design parameter and/or the observer model tuning parameter (e.g., the parameter that may be adjusted to affect a behavior of the system). 
     In the illustrated example of Equation (4) above, the variable ŷ(t) represents the estimate of the output vector, the variable C(t) represents an output matrix, where a dimension of C(t) is denoted by dim[C(t)]=p×n, and the variable {circumflex over (x)}(t) represents the estimate of the state vector, where {circumflex over (x)}(t) ∈ R n . In the illustrated example of Equation (4) above, the variable D(t) represents a feedthrough matrix (i.e., a feedforward matrix) where a dimension of D(t) is denoted by dim[D(t)]=p×m, and the variable u(t) represents the control vector or the input vector, where u(t) ∈ R. In some examples, the estimate of the state vector from Equation (3) is used to form the control feedback input u(t) applied to a plant (e.g., a mathematical representation of a physical system, longitudinal dynamics of an aircraft, etc.) through a gains matrix K as described in accordance with Equation (5) below: 
         u ( t )=− K{circumflex over (x)} ( t )   Equation (5)
 
     Inserting Equation (5) above into Equation (3) and Equation (4) above may result in an example observer model described in accordance with Equation (6) and Equation (7) below: 
         {dot over ({circumflex over (x)})} ( t )=( A ( t )− B ( t ) K ) {circumflex over (x)} ( t )+ L ( y ( t )− ŷ ( t ))   Equation (6)
 
         ŷ ( t )=( C ( t )− D ( t ) K ) {circumflex over (x)} ( t )   Equation (7)
 
     Due to the separation principle, the variables K and L may be chosen independently without disrupting the overall stability of the observer model. Advantageously, the variables K and L are effectively design variables that may be adjusted to improve performance of the observer model and that of the system. 
     An example vehicle controller and/or, more generally, an example vehicle control system, is/are disclosed herein for observer-based landing control of a vehicle. In some disclosed examples, the vehicle controller may be used to generate commands to control the vehicle. The example vehicle controller may generate or obtain a first command and modify the first command based on a state of a parameter of a vehicle, and/or, more generally, a state of the vehicle. For example, the vehicle controller may determine an adjustment, a modification, etc., to the first command based on a difference between a first vehicle state (e.g., an initial state) and a second vehicle state (e.g., a desired state, a predicted state, etc.). The example vehicle controller may calculate an estimate of a state for a parameter (e.g., a predicted output) in response to the vehicle executing the adjustment to the first command. The example vehicle controller may determine a second command based on the adjustment to the first command. The example vehicle controller may transmit the second command to a servomechanism (e.g., a heterostat, a mechanism to control a behavior of a system by manner of heterostasis, etc.) to execute the second command. The example vehicle controller may obtain a measurement from a sensor to determine a system output of the vehicle. For example, the vehicle controller associated with an aircraft may obtain an angular velocity measurement from a gyro sensor to estimate a state of an angle of attack parameter for the aircraft based on the aircraft or portion thereof executing a command (e.g., an adjusted command). 
     In some disclosed examples, the vehicle controller calculates a difference between the system output (e.g., the state of the vehicle parameter based on the measurement from the sensor) and the predicted output (e.g., the estimate of the state of the vehicle parameter). For example, the vehicle controller associated with an aircraft may determine a difference (e.g., an estimation error) between an estimate of a state for a vertical acceleration parameter for the aircraft and a measured state for the vertical acceleration parameter for the aircraft. The example vehicle controller may generate a third command based on the measurement from the sensor. The example vehicle controller may determine an adjustment to the third command based on at least one of the third command, the sensor measurement, or the estimation error. The example vehicle controller may determine a fourth command based on the adjustment to the third command. The example vehicle controller may transmit the fourth command to the servomechanism to effectuate the execution of the fourth command. 
     In some disclosed examples, the vehicle controller calculates an unknown state of a vehicle parameter and/or an unknown state of the vehicle based on a measurement from a sensor. For example, an aircraft may utilize one or more accelerometers to measure an acceleration of the aircraft and/or one or more angular rate sensors (e.g., gyro sensors) to measure angular velocity. The example vehicle controller may utilize measurements from one(s) of the accelerometers and/or one(s) of the gyro sensors to calculate a state of a parameter such as an angle of attack parameter, a pitch angle parameter, a pitch rate parameter, a sideslip parameter, etc. For example, an aircraft control system including the vehicle controller may estimate a value for the state of the angle of attack parameter for the aircraft based on the measurement(s) from the one(s) of the accelerometers, the one(s) of the gyro sensors, etc., as opposed to determining the value for the state of the angle of attack parameter for the aircraft based on a measurement from an angle of attack sensor. Alternatively, measurement(s) from sensor(s) of the aircraft may be used to determine any other parameter such as an airspeed parameter, an altitude parameter, a thrust parameter, etc. 
     In some disclosed examples, the vehicle controller identifies a phase of a flight plan, a flight route, etc., in which an aircraft is operating. For example, the flight plan may include one or more phases, regimes, segments, stages, etc., such as a parked flight stage, a taxi flight stage, a takeoff and departure flight stage, a climb flight stage, a cruise flight stage, a descent flight stage, an approach flight stage, a touchdown and roll-out flight stage, etc. In some disclosed examples, the approach flight segment or phase is referred to as a landing flare or round out. For example, the landing flare may be a maneuver that follows the approach (e.g., the final approach) stage and precedes the touchdown and roll-out stage of the landing. For example, during the flare regime, the nose of the aircraft may be raised to slow the descent rate and therefore create a softer touchdown. For example, during the flare regime, the aircraft may be controlled with a simultaneous increase in aircraft pitch attitude and a reduction in engine power (or thrust), the combination of which resulting in a decrease in both rate of descent and airspeed. 
     In some disclosed examples, the vehicle controller may enable observer-based control of an aircraft in response to determining that the aircraft has entered and/or otherwise transitioned into a flare regime of a flight plan. For example, the vehicle controller may effectuate automatic landing of the aircraft using one or more observer models as described herein. Advantageously, as described herein, the example vehicle controller may invoke and/or otherwise utilize the one or more observer models to enforce desired or intended levels of closed-loop stability, performance, and robustness. For example, the vehicle controller may control a flight control surface of the aircraft, and/or, more generally, the aircraft, by estimating a state of the flight control surface to facilitate control of the aircraft during the flare regime. Advantageously, the example vehicle controller may utilize the one or more observer models to estimate the state based on an attenuation of unknown flexible modes of the aircraft, reject disturbances from gusts, winds, or other weather phenomena, etc. 
     In some disclosed examples, the vehicle controller may include sub-modules to perform functions related to the control of the vehicle. For example, one or more of the sub-modules may be implemented with hardware, software, and/or firmware. The example sub-modules may be responsible for individual tasks such as obtaining information (e.g., network information, sensor information, etc.), determining a flight regime of a flight plan, generating a guidance command, determining a state of a parameter of the vehicle and/or the state of the vehicle, etc. The example sub-modules may be responsible for determining an estimate of a state of a parameter of the vehicle and/or an estimate of a state of the vehicle based on an execution of a command. In some examples, the sub-modules generate one or more control laws and calculate adjustments to a generated command. In some examples, the sub-modules transmit an adjusted generated command to a servomechanism to execute the adjusted generated command. 
       FIG. 1  is an illustration of an example aircraft  100  that includes a first example vehicle controller  102  to implement observer-based landing control of the aircraft  100 . For example, the first vehicle controller  102  may facilitate automatic landing of the aircraft  100  without human intervention during a flare regime or stage of a flight plan. The aircraft  100  is a commercial aircraft. Alternatively, the first vehicle controller  102  may be included in a different type of vehicle, such as a land-based vehicle, a marine-based vehicle, or a different type of air-based vehicle such as a UAV. 
     In the illustrated example of  FIG. 1 , the aircraft  100  includes wings  104 ,  106  coupled to a fuselage  108 . Engines  110 ,  112  are coupled to the wings  104 ,  106 . Slats  114 ,  116 , flaps  118 ,  120 , and ailerons  122 ,  124  are operatively coupled to the wings  104 ,  106 . Additional aircraft control surfaces of the aircraft  100  include horizontal stabilizers  126 ,  128 , elevators  130 ,  132 , and a vertical stabilizer  134 . In this example, the elevators  130 ,  132  are operatively coupled to respective ones of the horizontal stabilizers  126 ,  128 . In this example, the vertical stabilizer  134  is operatively coupled to a tail surface  136 , which is coupled to the fuselage  108 . 
     In the illustrated example of  FIG. 1 , the aircraft  100  includes a plurality of example sensors  138 ,  140 ,  142 ,  144 . The placement and quantity of the sensors  138 ,  140 ,  142 ,  144  are merely exemplary and not limited thereto. For example, the aircraft  100  may include fewer or more sensors  138 ,  140 ,  142 ,  144  than depicted and/or one(s) of the sensors  138 ,  140 ,  142 ,  144  may be located elsewhere on the aircraft  100 . The sensors  138 ,  140 ,  142 ,  144  include a first example sensor  138 , a second example sensor  140 , a third example sensor  142 , and a fourth example sensor  144 . The first sensor  138  is located proximate to and/or otherwise towards a nose of the aircraft  100 , such as by a cockpit  146  of the aircraft  100 . For example, the first sensor  138  may be a wireless sensor or a wired sensor. In some examples, the first sensor  138  may collect a pressure measurement (e.g., an air pressure measurement). For example, the first sensor  138  may be implemented by a pressure sensor such as a piezoelectric pressure sensor (e.g., a passive piezoelectric pressure sensor, a diaphragm pressure sensor, a pitot tube, etc. In some examples, the first sensor  138  is an acceleration sensor (e.g., an accelerometer), an angle of attack sensor, an angular rate sensor (e.g., a gyro sensor), an altitude sensor (e.g., an altimeter), a speed sensor, a temperature sensor, etc., or any other type of sensor that may monitor a parameter of the aircraft  100 . In some examples, measurement(s) from the first sensor  138  may be used to determine a parameter of the aircraft  100 , such as an altitude rate, a pitch rate, a pitch angle, etc., of the aircraft  100 . 
     The second sensor  140  is included in the second engine  112 . In some examples, the second sensor  140  may monitor and/or otherwise collect a measurement associated with the second engine  112 . For example, the second sensor  140  may be implemented by an acceleration sensor, an angular rate sensor, a pressure sensor, a speed sensor (e.g., an encoder, a proximity inductive sensor, etc., to measure a rotational speed of a turbine of the second engine  112 ), a temperature sensor (e.g., a sensor to measure a temperature of an inlet, an outlet, a compressor, etc., of the second engine  112 ), etc. In some examples, measurement(s) from the second sensor  140  may be used to determine a parameter of the aircraft  100 , such as an altitude rate, a pitch rate, a pitch angle, etc., of the aircraft  100 . 
     The third sensor  142  is included in the first horizontal stabilizer  126  to monitor and/or otherwise measure a parameter associated with the first elevator  130 . Alternatively, the third sensor  142  may be included in the first elevator  130 . The fourth sensor  144  is included in the second horizontal stabilizer  128  to monitor and/or otherwise measure a parameter associated with second elevator  132 . Alternatively, the fourth sensor  144  may be included in the second elevator  132 . The third sensor  142  and/or the fourth sensor  144  may be implemented with one or more position sensors, one or more skew position sensors, one or more electric power usage sensors (e.g., a voltage sensor, a current sensor, etc.), one or more hydraulic parameter sensors (e.g., a hydraulic flow rate sensor, a hydraulic pressure sensor, etc.), one or more motor speed sensors, etc. For example, the third sensor  142  may be implemented with one or more sensors to monitor and/or otherwise measure parameter(s) associated with a first actuator  148 . In some examples, the fourth sensor  144  may be implemented with one or more sensors to monitor and/or otherwise measure parameter(s) associated with a second actuator  150 . 
     In some examples, the first actuator  148  and/or the second actuator  150  is/are implemented with an electromechanical actuator, an electrohydraulic actuator, an electric backup hydraulic actuator, a hydraulic actuator, etc. For example, the first actuator  148  may be operatively coupled to the first elevator  130  to move the first elevator  130  from a stowed position to a deployed position, or any intermediate position between the stowed position and the deployed position. In some examples, the second actuator  150  is operatively coupled to the second elevator  132  to move the second elevator  132  from a stowed position to a deployed position, or any intermediate position between the stowed position and the deployed position. 
     In some examples, the actuators  148 ,  150  are motors (e.g., an electric motor, a hydraulic motor, etc.). In some examples, the actuators  148 ,  150  are operatively coupled to respective motors included in the horizontal stabilizers  126 ,  128  or the elevators  130 ,  132 . For example, the actuators  148 ,  150  may be implemented with one or more linear actuators (e.g., hydraulic or electric linear actuators), rotary actuators (e.g., hydraulic or electric rotary actuators), etc. In some examples, the first actuator  148 , when invoked and/or otherwise instructed, may control a motor associated with the first elevator  130  to cause the first elevator  130  to change or adjust positions. In some examples, the second actuator  150 , when invoked and/or otherwise instructed, may control a motor associated with the second elevator  132  to cause the second elevator  132  to change or adjust positions. 
     In some examples, the third sensor  142  may be implemented with a position sensor, a position skew sensor, etc., to measure a position of the first actuator  148  to determine a position of the first elevator  130 . In some examples, the third sensor  142  may be implemented with a voltage or current sensor to determine a power consumption associated with the first actuator  148 . In some examples, the third sensor  142  may be implemented with a hydraulic parameter sensor to measure a hydraulic parameter (e.g., a flow rate, a hydraulic fluid temperature, etc.) of the first actuator  148  in an example where the first actuator  148  is hydraulically powered or actuated. In some examples, the third sensor  142  may be implemented with a speed sensor (e.g., an actuator speed sensor, a motor speed sensor, etc.) to determine a speed at which the first actuator  148  is moving, a speed at which a motor operatively coupled to the first actuator  148  is rotating and/or otherwise moving, etc. 
     In some examples, the fourth sensor  144  may be implemented with a position sensor, a position skew sensor, etc., to measure a position of the second actuator  150  to determine a position of the second elevator  132 . In some examples, the fourth sensor  144  may be implemented with a voltage or current sensor to determine a power consumption associated with the second actuator  150 . In some examples, the fourth sensor  144  may be implemented with a hydraulic parameter sensor to measure a hydraulic parameter (e.g., a flow rate, a hydraulic fluid temperature, etc.) of the second actuator  150  in an example where the second actuator  150  is hydraulically powered or actuated. In some examples, the fourth sensor  144  may be implemented with a speed sensor (e.g., an actuator speed sensor, a motor speed sensor, etc.) to determine a speed at which the second actuator  150  is moving, a speed at which a motor operatively coupled to the second actuator  150  is rotating and/or otherwise moving, etc. In some examples, measurement(s) from the third sensor  142  and/or the fourth sensor  144  may be used to determine a parameter of the aircraft  100 , such as an altitude rate, a pitch rate, a pitch angle, etc., of the aircraft  100 . For example, a position of the first actuator  148 , the first elevator  130 , etc., may be used to determine the altitude rate, the pitch rate, the pitch angle, etc., of the aircraft  100 . 
     In the illustrated example of  FIG. 1 , the aircraft  100  includes the first vehicle controller  102  to perform observer-based control of one or more control surfaces of the aircraft  100 , and/or, more generally, the aircraft  100 . In this example, the first vehicle controller  102  is included in and/or otherwise located proximate a cockpit  146  of the aircraft  100 . Additionally or alternatively, the first vehicle controller  102  may have one or more components located elsewhere on the aircraft  100 . For example, the first vehicle controller  102  may be implemented using a distributed hardware, software, and/or firmware architecture. In such examples, a first hardware component (e.g., a processor, a memory device, an input/output (I/O) device, a network interface, etc.) may be included in the cockpit  146  while one or more second hardware components (e.g., a processor, a memory device, an I/O device, a network interface, etc.) may be included elsewhere on the aircraft  100 , such as in one of the wings  104 ,  106 , the fuselage  108 , one of the horizontal stabilizers  126 ,  128 , etc. In this example, there is only one instance of the first vehicle controller  102 . Alternatively, there may be more than one instance of the first vehicle controller  102  included in the aircraft  100 . 
     In the illustrated example of  FIG. 1 , the first vehicle controller  102  performs observer-based control of the aircraft  100 . For example, the first vehicle controller  102  may effectuated and/or otherwise cause control of the aircraft  100  based on one or more observer-models determining estimate(s) of state(s) of parameter(s) of the aircraft  100  based on sensor measurement(s) from one(s) of the sensors  138 ,  140 ,  142 ,  144 . In some examples, the first vehicle controller  102  may determine a first state of one or more control surfaces of the aircraft  100 , such as one(s) of the elevators  130 ,  132  during a flare regime of the flight plan executed by the aircraft  100 . For example, the first vehicle controller  102  may determine a first state of one(s) of the elevators  130 ,  132 , and/or, more generally, the aircraft  100  based on sensor measurement(s). In some examples, the first state may be determination(s) of an altitude rate, a pitch rate, a pitch angle, etc., and/or a combination thereof, of the aircraft  100  based on measurement(s) from the one(s) of the sensors  138 ,  140 ,  142 ,  144 . 
     In some examples, the first vehicle controller  102  may determine a second state (e.g., an estimate of a state) of the one or more control surfaces of the aircraft  100  based on the aircraft  100  executing a command (e.g., a landing command, a flare operation command, etc.). For example, the first vehicle controller  102  may determine the second state (e.g., the estimate of the state) of the one(s) of the elevators  130 ,  132  based on the one(s) of the elevators  130 ,  132  executing the command. In some examples, the second state may be an estimate of an altitude rate, a pitch rate, a pitch angle, etc., and/or a combination thereof, of the aircraft  100  by utilizing one or more observer-based models. The first vehicle controller  102  may also determine a third state (e.g., an updated estimate of the second state) of the one or more control surfaces of the aircraft  100  based on the difference between the first state and the second state. For example, the first vehicle controller  102  may also determine a third state of the elevators  130 ,  132 , and/or, more generally, the aircraft  100 , based on the difference between the first state and the second state of the elevators  130 ,  132 . In some examples, the first vehicle controller  102  may determine and/or generate a control input (e.g., a control input based on a baseline control input and/or an adaptive control input), which may implement a command to control the one or more control surfaces of the aircraft  100 , such as the elevators  130 ,  132 . For example, the first vehicle controller  102  may determine and/or generate the command to control the elevators  130 ,  132  (e.g., a control a position of the elevators  130 ,  132 ) based on the difference between the first state and the second state. In response to the generation of the command, the aircraft  100  may execute the command. For example, the elevators  130 ,  132  may move from a first position to a second position in response to the elevators  130 ,  132  executing the command. 
       FIG. 2  is an illustration of the example aircraft  100  of  FIG. 1  operating in an example flare regime  220  of an example flight plan  202 . In this example, the flight plan  202  includes one or more waypoints  206 ,  208  at which the aircraft  100  flies and/or otherwise moves along a flight path to execute the flight plan  202 . In this example, the aircraft  100  is at a first example waypoint  206  at which the aircraft  100  is at a preflare regime, stage, segment, etc., of the flight plan  202 . For example, the aircraft  100  may fly along an example preflare aircraft flight path  210 , which is implemented by a flight path between the first waypoint  206  and a second example waypoint  208 . 
     In the illustrated example of  FIG. 2 , the aircraft  100  engages and/or otherwise begins a flare operation at an altitude of the second waypoint  208 . For example, the first vehicle controller  102  of the aircraft  100  may determine that the aircraft  100  is at an altitude  212 , a portion of the flight plan  202 , etc., at which the aircraft  100  is to execute a landing flare or round out flight operation. In some examples, the first vehicle controller  102  may control the aircraft  100  to execute the flare operation at the second waypoint  208  by causing a nose of the aircraft  100  to rise to slow the descent rate and therefore create a softer touchdown at a touchdown location  214  within a touchdown zone  216  on a runway  218  or other ground surface. 
     In the illustrated example of  FIG. 2 , the portion of the flight plan  202  between the second waypoint  208  and the touchdown location  214  implements an example flare regime (e.g., a flare flight stage, a flare flight segment, etc.)  220  of the flight plan  202 . For example, the flare regime  220  may be based on a combination of the preflare aircraft flight path  210  and an example flare command path  222 . In such examples, the flare regime  220  implements a nominal aircraft trajectory to adjust an extrapolated flight path runway intersection  224  to the touchdown location  214  of the touchdown zone  216 . For example, during the flare regime  220 , the first vehicle controller  102  may control the aircraft  100  using one or more observer-based models to perform automatic landing control of the aircraft  100  with a simultaneous increase in aircraft pitch attitude and a reduction in engine power (or thrust) of the engines  110 ,  112  of  FIG. 1 , the combination of which may result in a decrease in both rate of descent and airspeed of the aircraft  100 . 
       FIG. 3  is a block diagram of an example implementation of a second example vehicle controller  300 . In some examples, the second vehicle controller  300  implements the first vehicle controller  102  of  FIG. 1 . The second vehicle controller  300  controls a vehicle, such as the aircraft  100  of  FIGS. 1 and/or 2 , with a generated command based on a measurement from a sensor, such as one(s) of the sensors  138 ,  140 ,  142 ,  144  of  FIG. 1 . In this example, the second vehicle controller  300  includes an example command input module  310 , an example observer module  320 , an example baseline control module  330 , an example vehicle module  340 , example sensor(s)  350 , an example network  360 , an example collection module  370 , an example datastore  380 , and an example error module  390 . 
     In the illustrated example of  FIG. 3 , the second vehicle controller  300  includes the command input module  310  to obtain or generate a command to control a vehicle. In some examples, the command input module  310  generates the command based on user input. For example, a pilot of the aircraft  100  may perform an action (e.g., maneuvering a joystick, pressing a button, annunciating a voice command, etc.) that the command input module  310  translates into the command to the baseline control module  330  and to the observer module  320 . In some examples, the command input module  310  generates the command based on a measurement from the sensor(s)  350 . For example, the command input module  310  may represent a guidance module (e.g., a guidance module of an unmanned aircraft (e.g., a UAV)) that generates the command for the baseline control module  330  to calculate the corresponding output and to move a control surface (e.g., one(s) of the flaps  118 ,  120 , one(s) of the elevators  130 ,  132 , etc., of  FIG. 1 ) of the aircraft  100  based on a measurement from the sensor(s)  350 . 
     In some examples, the command input module  310  generates the command based on information obtained from the datastore  380 . For example, the command input module  310  may generate the command based on a look-up table that includes commands based on the measurement from the sensor(s)  350 . For example, the command input module  310  may determine the measurement from the sensor(s)  350  and query the look-up table in the datastore  380  for the command corresponding to the measurement from the sensor(s)  350 . 
     In some examples, the command input module  310  determines a difference between a command (e.g., a guidance command) and a measurement from the sensor(s)  350 . For example, the command input module  310  may determine a first value (e.g., an initial command, an initial state of a parameter, an initial state of the vehicle, etc.). For example, the first value may be a guidance command r. The command input module  310  may determine a second value (e.g., a value obtained from the datastore  380 ). For example, the second value may be a measurement y or y meas  from the datastore  380 . The command input module  310  may determine a difference between the first value and the second value. For example, the command input module  310  may determine a difference between the command and the measurement to determine an error value of −e (e.g., r−y=−e). In some examples, the command input module  310  transmits the error value to the baseline control module  330 . 
     In the illustrated example of  FIG. 3 , the second vehicle controller  300  includes the observer module  320  to determine a state of a parameter of the vehicle, and/or, more generally, a state of the vehicle. In some examples, the observer module  320  utilizes one or more observer models. The one or more observer models may be mathematical representation(s) of the vehicle that provides an estimate of one or more internal states of the vehicle. The one or more observer models may determine the estimate of the one or more internal states of the vehicle based on a measurement of one or more inputs (e.g., commands) and/or outputs (e.g., sensors) of the vehicle. 
     In some examples, the observer module  320  determines a state of a vehicle parameter based on a measurement from the sensor(s)  350 . For example, the observer module  320  may determine a state of an angle of attack parameter of the aircraft  100  based on a measurement from an angle of attack sensor (e.g., from one(s) of the sensors  138 ,  140 ,  142 ,  144  of  FIG. 1 ). In some examples, the observer module  320  determines an estimate of the state of the vehicle parameter. For example, the observer module  320  may determine an estimate of the state of the angle of attack parameter of the aircraft  100  based on a measurement from a gyro sensor, a value (e.g., a sensor measurement, a value of a vehicle parameter state, etc.) from the datastore  380 , etc. The observer module  320  may obtain the measurement from the sensor(s)  350  from the collection module  370 . 
     In some examples, the observer module  320  determines an estimate for a state of a parameter of the vehicle based on the vehicle executing a command. For example, the observer module  320  may determine the state of a vehicle parameter before executing the command and calculate an estimate of the state of the vehicle parameter in response to executing the command. For example, the observer module  320  may determine a first value (e.g., an initial value) of a state of an angle of attack parameter of the aircraft  100 . The observer module  320  may calculate a second value (e.g., an estimate value) of the state of the angle of attack parameter of the aircraft  100  based on the aircraft  100  executing the command. The observer module  320  may calculate a first difference between the first value and the second value. 
     In some examples, the observer module  320  determines an estimate for a state of a parameter of the vehicle based on the vehicle executing a command during the flare regime  220  of  FIG. 2 . For example, the observer module  320  may determine the state of a parameter, such as an altitude, an altitude rate, a pitch rate, a pitch angle, etc., of the aircraft  100  at the second waypoint  208  before a control surface, such as the first elevator  130  of  FIG. 1 , executes a command to effectuate a flare operation of the aircraft  100 . For example, the command may correspond to a command generated by the first vehicle controller  102  and/or the second vehicle controller  300  to move the first elevator  130  from a first position to a second position. In some examples, during the flare regime  220 , the observer module  320  may calculate an estimate of the state of the parameter in response to the aircraft  100  executing the command. For example, the observer module  320  may determine a first value (e.g., an initial value) of the altitude, the altitude rate, the pitch rate, the pitch angle, etc. The observer module  320  may calculate a second value (e.g., an estimate value) of the state of the altitude, the altitude rate, the pitch rate, the pitch angle, etc., based on the first elevator  130 , and/or, more generally, the aircraft  100 , executing the command. The observer module  320  may calculate a first difference between the first value and the second value. 
     In some examples, the observer module  320  compares the first difference to an error estimation value calculated external to the observer module  320  to improve the observer module  320  state estimating functions. For example, the error estimation value may be calculated by the error module  390 . In some examples, the error estimation value may be calculated based on a second difference between (1) the value of the state of the parameter based on the measurement from the sensor(s)  350  and (2) the estimate value of the parameter calculated by the observer module  320 . For example, the parameter may be a pitch rate of the aircraft  100 , the value of the state of the parameter may be 5 degrees, and the estimate value of the parameter may be 3 degrees. 
     In some examples, the observer module  320  transmits the estimate value of the state of the parameter to the error module  390 . In some examples, the observer module  320  determines whether the first difference and/or the second difference satisfies a threshold. For example, the observer module  320  may determine that the first difference (e.g., 2 degrees) does not satisfy a threshold (e.g., 1 degree, 0.5 degrees, etc.). In some examples, the observer module  320  may determine that the first difference does not satisfy the threshold because the first difference is less than the threshold. In some examples, the observer module  320  may determine that the first difference satisfies the threshold because the first difference is greater than the threshold. In some examples, the observer module  320  may determine that the second difference (e.g., 3 degrees) satisfies the threshold because the second difference is greater than the threshold. In some examples, the observer module  320  may determine that the second difference does not satisfy the threshold because the second difference is less than the threshold. 
     In some examples, the observer module  320  determines an estimate of a state of a parameter of a vehicle, and/or, more generally, a state of the vehicle based on an obtained command. For example, the observer module  320  may determine an estimate of a state of a sideslip parameter of the aircraft  100  based on a command obtained from the command input module  310 . The observer module  320  may determine the estimate of the state based on the command obtained from the command input module  310 , the measurement from the sensor(s)  350 , the error estimation obtained by the observer module  320 , etc. For example, the observer module  320  may determine a first value (e.g., an initial value) for a state of a parameter of the aircraft  100 . The observer module  320  may additionally determine a second value (e.g., an estimate value) for the state of the parameter based on the aircraft  100  executing the command obtained from the command input module  310 . The observer module  320  may also determine a third value (e.g., an updated estimate of the state of the vehicle parameter) based on the difference between the first value and the second value. In some examples, the observer module  320  determines the third value in response to at least one of the first difference or the second difference as described above satisfying one or more thresholds. In some examples, the observer module  320  transmits the third value (e.g., the updated estimate of the state of the parameter) to the baseline control module  330 . 
     In some examples, the observer module  320  performs a squaring-up modification to an input matrix and/or an output matrix of the one or more observer models utilized and/or otherwise implemented by the observer module  320 . In some examples, the observer module  320  adds a pseudo-output matrix to the output matrix of the one or more observer models. In some examples, the observer module  320  adds a pseudo-input matrix to the input matrix of the one or more observer models. For example, the observer module  320  may add the pseudo-input matrix, which may include fictitious inputs (e.g., inputs that do not represent physical inputs to the vehicle), to the input matrix of the one or more observer models to make a number of inputs (e.g., controls) in the input matrix equal a number of outputs (e.g., measurements) in the output matrix. In some examples, the observer module  320  makes the one or more observer models used by the observer module  320  minimum phase (e.g., the vehicle transmission zeros are located in C − ) by performing the squaring-up modification(s). During the squaring-up modification(s), the observer module  320  may place one or more zeros (e.g., transmission zeros) in a desired location utilizing a linear quadratic regulator (LQR) and/or a pole-placement algorithm or technique. The observer module  320  may perform the squaring-up modification(s) to satisfy one or more sufficient conditions. A first sufficient condition may be a relationship of p=m, where p represents a number of outputs and m represents a number of inputs. For example, the first sufficient condition may represent square dynamics of the one or more observer models used by the observer module  320 . A second sufficient condition may be a relationship of det (CB) ≠ 0, where a determinant of an output matrix C and an input matrix B does not equal zero. For example, the second sufficient condition may represent a relative degree of one. A third sufficient condition may be a relationship of det 
     
       
         
           
             
               ( 
               
                 
                   
                     
                       sI 
                       - 
                       A 
                     
                   
                   
                     B 
                   
                 
                 
                   
                     C 
                   
                   
                     0 
                   
                 
               
               ) 
             
             = 
             0 
           
         
       
     
     where s ∈ C − . For example, the third sufficient condition may include a determinant of a matrix including the input matrix B, the output matrix C, and a transfer function sI−A, where the determinant of the matrix equals zero, and where all zeros (e.g., transmission zeros) are in the open left half of the complex plane of the output matrix C (excluding the jw-axis). For example, the third sufficient condition may represent and/or otherwise indicate that the observer module  320  uses the one or more observer models that include one or more transmission zeros that are stable. In some examples, the third sufficient condition may represent that the observer module  320  uses the one or more observer models representing a system that is minimum phase. 
     In some examples, the observer module  320  performs the squaring-up modification(s) by converting a tall system to a square system. For example, a tall, controllable, observable, and minimum-phase system with full rank C meas *B may be squared-up to satisfy the first, second, and third example sufficient conditions as described above, where the variable C meas  represents the output matrix 
     
       
         
           
             
               ( 
               
                 
                   
                     
                       I 
                       mxm 
                     
                   
                   
                     0 
                   
                 
                 
                   
                     0 
                   
                   
                     
                       C 
                       
                         p 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         meas 
                       
                     
                   
                 
               
               ) 
             
             . 
           
         
       
     
     An example tall system is described in Equation (8) below: 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           A 
                         
                         
                           B 
                         
                       
                       
                         
                           
                             C 
                             meas 
                           
                         
                         
                           
                             0 
                             
                               p 
                               × 
                               m 
                             
                           
                         
                       
                     
                     ) 
                   
                   ∈ 
                   
                     R 
                     
                       
                         ( 
                         
                           n 
                           + 
                           p 
                         
                         ) 
                       
                       × 
                       
                         ( 
                         
                           n 
                           + 
                           m 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     8 
                     ) 
                   
                 
               
             
           
         
       
     
     In the illustrated example of Equation (8) above, variables A and B represent m-Inputs, variables C meas  and 0 p×m  represent p-Outputs, and the variable n represents the number of states. The observer module  320  may convert the example tall system described above in Equation (8) into an example square system as described in Equation (9) below: 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         
                           A 
                         
                         
                           
                             ( 
                             
                               B 
                               , 
                               
                                 B 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                       
                         
                           
                             C 
                             meas 
                           
                         
                         
                           
                             0 
                             
                               p 
                               × 
                               p 
                             
                           
                         
                       
                     
                     ) 
                   
                   ∈ 
                   
                     R 
                     
                       
                         ( 
                         
                           n 
                           + 
                           p 
                         
                         ) 
                       
                       × 
                       
                         ( 
                         
                           n 
                           + 
                           p 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
           
         
       
     
     In the illustrated example of Equation (9) above, the variables A and (B, B 2 ) represent p-Inputs, the variables C meas  and 0 p×p  represent p-Outputs, and the variable n represents the number of states. As described in Equation (9) above, the observer module  320  may add one or more fictitious inputs to the input matrix of B to yield a second input matrix (B, B 2 ), where B 2  is a pseudo-input matrix. The observer module  320  may replace the input matrix of B with the second input matrix (B, B 2 ) in the first, second, and third example sufficient conditions as described above. The observer module  320  may satisfy the first, second, and third example sufficient conditions due to the following revised relationships 
     
       
         
           
             
               
                 B 
                 _ 
               
               = 
               
                 
                   ( 
                   
                     B 
                     , 
                     
                       B 
                       2 
                     
                   
                   ) 
                 
                 → 
                 
                   
                     det 
                     ⁡ 
                     
                       ( 
                       
                         
                           C 
                           meas 
                         
                         ⁢ 
                         
                           B 
                           _ 
                         
                       
                       ) 
                     
                   
                   ≠ 
                   
                     0 
                     ⋀ 
                     
                       ( 
                       
                         
                           
                             det 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     
                                       sI 
                                       - 
                                       A 
                                     
                                   
                                   
                                     
                                       B 
                                       _ 
                                     
                                   
                                 
                                 
                                   
                                     
                                       C 
                                       meas 
                                     
                                   
                                   
                                     0 
                                   
                                 
                               
                               ) 
                             
                           
                           = 
                           0 
                         
                         , 
                         
                           
                             → 
                             s 
                           
                           ∈ 
                           
                             C 
                             - 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             , 
           
         
       
     
     where the revised relationships are determined by at least Equation (9) above. For example, the revised relationships may represent that the pseudo-input matrix B 2  generated during the squaring-up modification(s) satisfy the first, second, and third example sufficient conditions as described above. As a result, the observer module  320  may utilize the input matrix  B  in the one or more observer models to perform observer-based landing control of the aircraft  100  during a stage of a flight plan, such as the flare regime  220  of the flight plan  202  of  FIG. 2 . 
     In some examples, the observer module  320  determines one or more symmetric, positive, definite, and parameter-dependent weight matrices for the one or more observer models. For example, the observer module  320  may assign Q 0  ∈ R n×n  and R 0  ∈ R m×m  to be symmetric and positive definite, where R n×n  denotes the space of all n×n matrices, and where R m×m  denotes the space of all m×m matrices. The observer module  320  may determine one or more constants within R n×n  and/or R m×m . For example, the observer module  320  may determine a value for constants v and/or η, where v&gt;0 and η&gt;0. The observer module  320  may determine two symmetric, positive, definite, and parameter-dependent weight matrices as described in Equation (10) and Equation (11) below: 
     
       
         
           
             
               
                 
                   
                     Q 
                     v 
                   
                   = 
                   
                     
                       Q 
                       0 
                     
                     + 
                     
                       
                         ( 
                         
                           
                             v 
                             + 
                             1 
                           
                           v 
                         
                         ) 
                       
                       ⁢ 
                       
                         B 
                         _ 
                       
                       ⁢ 
                       
                         
                           B 
                           _ 
                         
                         T 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     10 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     R 
                     v 
                   
                   = 
                   
                     
                       v 
                       
                         v 
                         + 
                         1 
                       
                     
                     ⁢ 
                     
                       R 
                       0 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     11 
                     ) 
                   
                 
               
             
           
         
       
     
     The observer module  320  may use at least one of the constants v and/or η, Equation (10) above, or Equation (11) above to evaluate a parameter-dependent Algebraic Riccati Equation (ARE) as described in Equation (12) below: 
         P   v ( A+ηI   n×n ) T +( A+ηI   n×n ) P   v   −P   v   C   meas   T   R   v   −1   C   meas   P   v   +Q   v =0   Equation (12)
 
     In the illustrated example of Equation (12) above, the variable P v  represents the unique, symmetric, positive, and definite solution for any positive value of the constants v and η. In the illustrated example of Equation (12) above, the variable A represents the observer matrix included in the one or more observer models utilized by the observer module  320 , and the variable I n×n  represents an identity matrix of size n×n. In some examples, the observer module  320  evaluates the asymptotic behavior of P v  as v→0 while holding η fixed. For example, the observer module  320  may use the asymptotic expansion as described below in Equation (13) to determine one or more asymptotic relations as described in Equation (14), Equation (15), and Equation (16) as described below where the variable O represents Bachmann-Landau asymptotic order notation: 
     
       
         
           
             
               
                 
                   
                     P 
                     v 
                   
                   = 
                   
                     
                       P 
                       0 
                     
                     + 
                     
                       
                         P 
                         1 
                       
                       ⁢ 
                       v 
                     
                     + 
                     
                       O 
                       ⁡ 
                       
                         ( 
                         
                           v 
                           2 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     13 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     P 
                     v 
                   
                   = 
                   
                     
                       P 
                       0 
                     
                     + 
                     
                       O 
                       ⁡ 
                       
                         ( 
                         v 
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     14 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     P 
                     v 
                     
                       - 
                       1 
                     
                   
                   = 
                   
                     
                       P 
                       0 
                       
                         - 
                         1 
                       
                     
                     + 
                     
                       O 
                       ⁡ 
                       
                         ( 
                         v 
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     15 
                     ) 
                   
                 
               
             
             
               
                 
                   
                     
                       P 
                       v 
                       
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                       B 
                       _ 
                     
                   
                   = 
                   
                     
                       
                         C 
                         meas 
                         T 
                       
                       ⁢ 
                       
                         R 
                         0 
                         
                           - 
                           
                             1 
                             2 
                           
                         
                       
                       ⁢ 
                       W 
                     
                     + 
                     
                       O 
                       ⁡ 
                       
                         ( 
                         v 
                         ) 
                       
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     16 
                     ) 
                   
                 
               
             
           
         
       
     
     In some examples, the observer module  320  evaluates the asymptotic expansion described above in Equation (13) to determine the asymptotic relations as described above in Equation (14), Equation (15), and Equation (16) as v→0, with a constant, symmetric, positive, and definite matrix P 0 . In some examples, the observer module  320  evaluates Equation (16) above by applying a relationship of W=(UV) T , where the two unitary matrices, U and V, are defined by the singular value decomposition as described in Equation (17) below: 
           B     T   C   meas   T   R   0   −½   =UΣV    Equation (17)
 
     In the illustrated example of Equation (17) above, the notation represents the diagonal matrix of the corresponding singular values. In some examples, Equation (16) above and Equation (17) above guarantee strict positive definiteness of P v  and P v   −1  uniformly in v. The observer module  320  may utilize one or more of the above-described equations to determine the observer gain L v  as described in Equation (18) below: 
         L   v   =P   v   C   meas   T   R   v   −1    Equation (18)
 
     In the illustrated example of Equation (18) above, the variable P v  represents the unique solution described above in Equation (12), where P v =P v   T &gt;0. The observer module  320  may utilize the relationship described above in Equation (18) to determine the closed-loop observer dynamics of the observer model of a system (e.g., a vehicle, the aircraft  100 , etc.) as described in Equation (19) and Equation (20) below: 
         {dot over ({circumflex over (x)})}=A{circumflex over (x)}+Bu   bl   +B   cmd   y   cmd   +L   v ( y   meas   −ŷ   meas )   Equation (19)
 
       ŷ meas =C meas {circumflex over (x)}  Equation (20)
 
     In the illustrated example of Equation (19) above, the variable {dot over ({circumflex over (x)})} represents an estimate of an observer state derivative vector, the variable A represents a state matrix, and the variable {circumflex over (x)} represents an estimate of a state vector. Further, in the illustrated example of Equation (19) above, the variable B represents an input matrix, the variable B cmd  represents an input command matrix, and the variable y cmd  represents an output command vector. In the illustrated example of Equation (19) above, the variable L v  represents the observer gain, the variable y meas  represents a measured output vector (e.g., a measurement from a sensor), and the variable ŷ meas  represents an estimate of a measured output vector. Additionally, in the illustrated example of Equation (19) above, the variable u bl  represents a baseline control input or a baseline control command (e.g., a value generated by the baseline control module  330 ), where u bl  may be described in accordance with Equation (21) below: 
         u   bl   =−K   lqr   {circumflex over (x)}   Equation (21)
 
     In the illustrated example of Equation (21) above, the variable K lqr  represents a constant Linear Quadratic Regulator (LQR) baseline control gain, where K lqr  ∈ R n×m . In Equation (20) above, the variable C meas  represents a measured output matrix. Further, in Equation (20) above, the measured output vector ŷ meas  tracks the bounded command y cmd  described above in Equation (19) with uniformly bounded errors. 
     The observer module  320  may determine the variable K lqr  such that an observer state matrix A obs  described below in Equation (22) becomes Hurwitz (e.g., every eigenvalue of A obs  has a strictly negative real part) and has one or more desired modal characteristics: 
         A   obs   =A−BK   lqr   −L   v   C   meas    Equation (22)
 
     The observer module  320  may apply Equation (22) above to Equation (20) above to yield Equation (23) as described below: 
         {dot over ({circumflex over (x)})}=A   obs   {circumflex over (x)}+B   cmd   y   cmd   +L   v   y   meas    Equation (23)
 
     In some examples, the observer module  320  determines and/or otherwise evaluates the relationship as described above in Equation (23) to recover LQR full state baseline feedback stability margins at the input to the vehicle plant. In some instances, the observer module  320  determines a value of the constant v to be sufficiently small to recover the LQR stability margins at the input to the one or more observer models and/or the vehicle plant. 
     In the illustrated example of  FIG. 3 , the second vehicle controller  300  includes the baseline control module  330  to generate a control input to control the vehicle, such as the aircraft  100  of  FIGS. 1 and/or 2 . For example, the baseline control module  330  may generate a value for a control input variable u to control a control surface, such as one of the flaps  118 ,  120 , one of the ailerons  122 ,  124 , one of the elevators  130 ,  132 , etc., of the aircraft  100 . In some examples, the baseline control module  330  generates the control input based on a guidance command obtained from the command input module  310 . In some examples, the baseline control module  330  generates the control input based on an estimate of a state of the vehicle obtained from the observer module  320  and/or an estimate of a state of a parameter of the vehicle obtained from the observer module  320 . 
     In some examples, the baseline control module  330  includes integral error control mechanisms such as, for example, an integral controller transfer function representative of a servomechanism. The baseline control module  330  may obtain a guidance command r and/or an error value −e from the command input module  310 . The baseline control module  330  may utilize an integral controller transfer function 
     
       
         
           
             
               
                 K 
                 i 
               
               s 
             
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     or a logic circuit to implement the integral controller transfer function 
     
       
         
           
             
               
                 K 
                 i 
               
               s 
             
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     to generate a baseline command utilized to generate the control input u. For example, the baseline control module  330  may apply the integral controller transfer function to the obtained guidance command (or pass through the obtained guidance command through a logic circuit that implements the integral controller transfer function) to generate and/or otherwise output the baseline command. In some examples, the baseline control module  330  determines a difference between the baseline state of a parameter (e.g., the baseline command) and an estimate of a state of the parameter obtained from the observer module  320  (e.g., a state feedback stability value K x , where x represents the state and/or the estimate of the state) to determine the control input u. The baseline control module  330  may determine the control input u as described in Equation (24) below: 
         u=−K   lqr   {circumflex over (x)}   Equation (24)
 
     In the illustrated example of Equation (24) above, the variable K w , represents the constant LQR baseline control gain, where K lqr  ∈ R n×m , and the variable {circumflex over (x)} represents the estimate of the state vector. The baseline control module  330  may further expand the relationship as described above in Equation (24) by replacing the variable {circumflex over (x)} in Equation (25) below: 
         u=−K   lqr ( sI   n×n   −A   obs ) −1 ( B   cmd   y   cmd   +L   v   y   meas )   Equation (25)
 
     In the illustrated example of Equation (25) above, the term (sI n×n −A obs ) −1  represents the transfer function of the one or more observer models utilized by the observer module  320 . The baseline control module  330  may determine the control input u based on Equation (25) above. 
     In the illustrated example of  FIG. 3 , the second vehicle controller  300  includes the vehicle module  340  to execute a command of the vehicle. The vehicle module  340  may include and/or otherwise implement a plant (e.g., a system) represented by one or more transfer functions, where the transfer functions may be mathematical representations utilized to describe inputs and outputs of the vehicle. The vehicle module  340  may include the plant to combine a process and an actuator. For example, the vehicle module  340  may include the plant to represent a control surface (e.g., one of the slats  114 ,  116 , one of the flaps  118 ,  120 , one of the elevators  130 ,  132 , etc.) of the aircraft  100 . The plant may include a transfer function to represent an actuator and/or a sensor monitoring the actuator of the aircraft control surface. For example, the plant may include a transfer function to represent one(s) of the actuators  148 ,  150  and/or one(s) of the third sensor  142  and/or the fourth sensor  144  monitoring the actuators  148 ,  150  of the elevators  130 ,  132 . 
     In some examples, the plant corresponds to and/or otherwise represents plant dynamics. For example, the plant may correspond to aircraft longitudinal dynamics of the aircraft  100 . In such examples, the aircraft longitudinal dynamics may be implemented with one or more longitudinal flight equations of motion. For example, the aircraft longitudinal dynamics may correspond to a first velocity of the aircraft  100  along a body axis of the aircraft  100 , a second velocity of the aircraft  100  perpendicular to the body axis of the aircraft  100 , an angle (e.g., a body angle) between the body axis and the horizontal axis of the aircraft  100 , an angular velocity of the aircraft  100 , etc., and/or a combination thereof 
     In some examples, the vehicle module  340  may invoke the plant to determine an elevator angle associated with one(s) of the elevators  130 ,  132  of  FIG. 1 . For example, the vehicle module  340  may determine the elevator angle based on a measurement from a position sensor (e.g., the third sensor  142  of  FIG. 1 ) monitoring the first elevator  130 . In some examples, the vehicle module  340  may determine a thrust of the aircraft  100  based on a thrust generated by the engines  110 ,  112  of  FIG. 1 . For example, the vehicle module  340  may determine the thrust based on a measurement from a pressure sensor, a temperature, etc., and/or a combination thereof (e.g., the second sensor  140  of  FIG. 1 ). In some examples, the vehicle module  340  may invoke the plant to determine the first velocity and/or the second velocity of the aircraft  100  based on the thrust. In some examples, the vehicle module  340  may invoke the plant to determine the body angle of the aircraft  100  based on the elevator angle. In some examples, the vehicle module  340  may invoke the plant to determine the angular velocity of the aircraft  100  based on at least one of the elevator angle or the thrust. In some examples, the vehicle module  340  may invoke the plant to determine the longitudinal dynamics of the aircraft  100  based on at least one of the first velocity, the second velocity, the body angle, or the angular velocity. 
     In some examples, the vehicle module  340  includes one or more state-space relationships. The vehicle module  340  may obtain the control input (e.g., the control input u) from the baseline control module  330 . The vehicle module  340  may achieve bounded command tracking in the vehicle. For example, the vehicle module  340  may evaluate the one or more state-space relationships using the control input u to determine a regulated output y reg  to follow the external bounded time-varying command y cmd . The vehicle module  340  may be represented by and/or otherwise implement the state-space relationships as described below in Equation (26), Equation (27), and Equation (28): 
         {dot over (x)}=Ax+B Λ( u+ΘO   T Φ( x ))+ B   ref   y   cmd    Equation (26)
 
       y=Cx   Equation (27)
 
       y reg =C reg x   Equation (28)
 
     For example, the vehicle module  340  may include one or more logic circuits that implement the state-space relationships as described above in Equation (26), Equation (27), and/or Equation (28). In the illustrated example of Equation (26) above, the state matrix A, the input matrix B, and the reference input matrix B ref , are known matrices, where A ∈ R n×n , (B,B ref ) ∈ R n×m . In some examples, (A, B) is controllable and rank B=m (i.e., B has full column rank). In some instances, (A, C) is observable and rank C=p (i.e., C has full row rank). In some examples, the number of outputs (e.g., measured outputs) is greater than the number of inputs (e.g., control inputs) (i.e., p&gt;m) where rank (CB)=m. In the illustrated example of Equation (26) above, the system state is x ∈ R n , and the control input is u ∈ R m . Further, in the illustrated example of Equation (26) above, the variable Λ is a constant unknown non-singular positive diagonal matrix representing the system uncertainties where Λ ∈ R m×m . Additionally, in the illustrated example of Equation (26) above, the variable Θ is a constant unknown matrix where Θ ∈ R n×m , and the variable Φ represents a known regressor vector where Φ ∈ R n . In some examples, the regressor is globally Lipschitz continuous in x, where there exists a finite positive known constant 0&lt;L Φ &lt;∞, such that the relationship described below in Equation (29) holds true for any x 1 , x 2  ∈ R n : 
       ∥Φ( x   1 )−Φ( x   2 )∥≤ L   Φ   ∥x   1   −x   2 ∥  Equation (29)
 
     In the illustrated examples of Equation (27) above and Equation (28) above, the output matrix C and the regulated output matrix C reg  are known matrices, where C ∈ R p×n  and C reg  ∈ R m×n . In the illustrated examples of Equation (27) above and Equation (28) above, the system measurements are grouped into y ∈ R p , the regulated output is y reg  ∈ R m , and y cmd  ∈ R m  denotes the external bounded time-varying command for y reg  to track. In the illustrated example of Equation (28) above, the regulated output dynamics (e.g., the regulated outputs y reg ) may be non-minimum phase and have a vector relative degree greater than unity. 
     In the illustrated example of  FIG. 3 , the second vehicle controller  300  includes the sensor(s)  350  to obtain measurement(s) of the vehicle. For example, the sensor(s)  350  may implement, include, and/or otherwise correspond to one or more sensors of a vehicle, such as the aircraft  100 . For example, the sensor(s)  350  may monitor, determine, and/or otherwise measure a state of an output of the aircraft  100 . In some examples, the output may be a state of a parameter such as, for example, an angle of attack, a pitch angle, a pitch rate, a first flex mode position, a second flex mode position, a first flex mode velocity, a second flex mode velocity, etc., of a control surface of the aircraft  100 , and/or, more generally, the aircraft  100 . The output measurement may also be represented as a linear combination of the states such as vertical acceleration. In some examples, the sensor(s)  350  implement one(s) of the sensors  138 ,  140 ,  142 ,  144  of  FIG. 1 . For example, the sensor(s)  350  may be implemented with one or more sensors such as an accelerometer, an altimeter, a gyro sensor, a pressure sensor, a speed sensor, a temperature sensor, etc. Additionally or alternatively, the sensor(s)  350  may be implemented with any number of and/or types of sensors operating on the aircraft  100 , a land-based vehicle, or marine-based vehicle. 
     In the illustrated example of  FIG. 3 , the second vehicle controller  300  includes the network  360 . The sensor(s)  350  may be in communication with the network  360 . The network  360  of the illustrated example of  FIG. 3  may implement a process control network (e.g., an aircraft process control network, a vehicle network, etc.). However, the example network  360  may be implemented using any suitable wired and/or wireless network(s) including, for example, one or more data buses, one or more aircraft process control networks, one or more Local Area Networks (LANs), one or more wireless LANs, one or more cellular networks, one or more private networks, one or more public networks, etc. The network  360  enables the sensor(s)  350  to be in communication with the collection module  370 . 
     In the illustrated example of  FIG. 3 , the second vehicle controller  300  includes the collection module  370  to query, filter, obtain, process, and/or select a measurement. In some examples, the collection module  370  obtains measurement(s) from the sensor(s)  350  via the network  360 . In some examples, the collection module  370  obtains the measurement(s) from the sensor(s)  350  directly (e.g., without the network  360 ). The collection module  370  may obtain unprocessed information (e.g., non-manipulated data from the sensor(s)  350 , non-scaled data from the sensor(s)  350 , etc.) or processed information (e.g., manipulated data from the sensor(s)  350 , scaled data from the sensor(s)  350 , etc.). In some examples, the collection module  370  stores sensor information (e.g., sensor data, sensor measurement(s), etc.) in the datastore  380 . 
     In some examples, the collection module  370  selects obtained sensor measurements of interest to be used by one or more algorithms, processes, programs, techniques, etc. deployed by the second vehicle controller  300 . For example, the collection module  370  may process a value from a sensor measurement by converting (e.g., converting using a conversion calculation, converting to different units of measure, etc.), scaling (e.g., scaling using a scaling factor), and/or translating (e.g., translating using a pre-determined curve, translating using a pre-determined equation) the value from the sensor measurement for use by the observer module  320  and, more generally, the second vehicle controller  300 . In some examples, the collection module  370  selects the sensor measurement by querying the datastore  380 . In response to the datastore  380  receiving the query sent from the collection module  370 , the datastore  380  transmits the sensor measurement to the collection module  370 . In some examples, the collection module  370  obtains a query from the observer module  320  and/or the error module  390  for a sensor measurement of interest. In response to the collection module  370  receiving the query, the collection module  370  may transmit the sensor measurement of interest to the observer module  320  and/or the error module  390 . 
     In the illustrated example of  FIG. 3 , the second vehicle controller  300  includes the datastore  380  to record data (e.g., obtained sensor information, calculated sensor measurement values, look-up tables, etc.). In some examples, the datastore  380  stores a pre-defined look-up table that includes values for gain parameters. For example, observer module  320  and/or the baseline control module  330  may query the look-up table in the datastore  380  to obtain a gain value to be used in one or more calculations. In some examples, the look-up table may store and/or otherwise include associations, relationships, etc., between values of parameters and gain values. For example, the observer module  320  may identify a gain value by mapping a value of a parameter to a first association in the look-up table between the value of the parameter and the gain value. 
     In some examples, the datastore  380  may be implemented by a volatile memory (e.g., a Synchronous Dynamic Random Access Memory (SDRAM), Dynamic Random Access Memory (DRAM), RAIVIBUS Dynamic Random Access Memory (RDRAM), etc.) and/or a non-volatile memory (e.g., flash memory). The datastore  380  may additionally or alternatively be implemented by one or more double data rate (DDR) memories, such as DDR, DDR2, DDR3, mobile DDR (mDDR), etc. The datastore  380  may additionally or alternatively be implemented by one or more mass storage devices such as hard disk drive(s) (HDD(s)), compact disk (CD) drive(s), digital versatile disk (DVD) drive(s), magnetic media, etc. While in the example the datastore  380  is illustrated as a single datastore, the datastore  380  may be implemented by any number and/or type(s) of datastores. 
     In the illustrated example of  FIG. 3 , the second vehicle controller  300  includes the error module  390  to determine an error estimation value. In some examples, the error module  390  may calculate a difference between a measured (true or known) value of a state of a parameter and an estimate value of the state of the parameter. For example, the error module  390  may obtain the measured value from the collection module  370 . In such examples, the error module  390  may identify a first value of a state of a pitch rate of the aircraft  100 , where the first value is measured from one of the sensors  138 ,  140 ,  142 ,  144 , such as a gyro sensor. In some examples, the error module  390  may identify a second value of the state of the pitch rate of the aircraft  100 , where the second value is an estimate value of the state of the pitch rate obtained from the observer module  320 . In some examples, the error module  390  may determine a difference (e.g., an error estimation value) between the first value and the second value. In response to the error module  390  determining the difference, the error module  390  may transmit the difference to the observer module  320 . For example, the error module  390  may transmit, deliver, and/or otherwise provide the error estimation value to the observer module  320  to improve the state estimating functions of the observer module  320 , and/or, more generally, improve control of flight operations of the aircraft  100 , such as a flight operation during the flare regime  220  of  FIG. 2 . 
       FIG. 4  is a block diagram of an example implementation of a third example vehicle controller  400 . In some examples, the third vehicle controller  400  may be an example implementation of the first vehicle controller  102  of  FIG. 1 , and/or the second vehicle controller  300  of  FIG. 3 . In some examples, the third vehicle controller  400  controls a vehicle, such as the aircraft  100  of  FIGS. 1 and/or 2 , with a generated command based on measurement(s) from one or more sensors (e.g., one(s) of the sensors  138 ,  140 ,  142 ,  144  of  FIG. 1 ). For example, the third vehicle controller  400  may control one or more control surfaces of the aircraft  100  with a generated control surface command based on measurement(s) from one(s) of the sensors  138 ,  140 ,  142 ,  144 . 
     In the illustrated example of  FIG. 4 , the third vehicle controller  400  includes an example observer module  410  and an example baseline control module  420 . In some examples, the observer module  410  is an example implementation of the observer module  320  of  FIG. 3 . In some examples, the baseline control module  420  is an example implementation of the baseline control module  330  of  FIG. 3 . Additionally or alternatively, the third vehicle controller  400  may include one(s) of the command input module  310 , the observer module  320  (e.g., to implement a dual-observer model of the vehicle), the vehicle module  340 , the sensor(s)  350 , the network  360 , the collection module  370 , the datastore  380 , and/or the error module  390  of  FIG. 3 . 
     In the illustrated example of  FIG. 4 , the third vehicle controller  400  includes the observer module  410  to at least determine a control input to the baseline control module  420 . The observer module  410  obtains a bounded command y cmd . In some examples, the observer module  410  obtains the bounded command y cmd  from a command input module such as, for example, the command input module  310  from  FIG. 3 . In this example, the variable B cmd  represents a gain command value, the transfer function (sI n×n −A obs ) −1  represents a transfer function of the observer model utilized by the observer module  410 , and the variable {circumflex over (x)} represents the estimate of the state vector. In this example, the variable I n×n  represents an identity matrix of size n×n. The designator obs in the observer module  410  is representative of and/or otherwise indicates the observer model. For example, the variable A obs  represents a state matrix of the observer model. In this example, the variable K lqr  represents a LQR constant gain and the variable L v  represents the observer error feedback gain. In this example, the variable e yI  represents an output observation error based on a difference of the variables y reg  and y cmd  applied to an integrator transfer function 
     
       
         
           
             
               1 
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     The variable y reg  represents a regulated output of the baseline control module  420  based on the control input u generated by the observer module  410 . 
     In the illustrated example of  FIG. 4 , the third vehicle controller  400  includes the variable u to represent the control input. In some examples, the control input u includes and/or otherwise implements the adaptive control input u ad  as described above. In this example, the control input u is represented by a relationship as described by an equation in block  430 , where the control input u is based on the LQR gain K lqr  and the estimate of the state vector {circumflex over (x)}. In block  430 , the variable y meas  represents a measured output of the third vehicle controller  400 . In this example, the measured output y meas  may also represent the input to the observer error feedback gain L v . The measured output y meas  may be represented by the mathematical relationships as described in block  440 . 
     In the illustrated example of block  440 , the measured output y meas  is based on the output observation error e yI  and the measured plant output y p meas . The output observation error e yI  may be based on the identity matrix I m×m , where the identity matrix is size m×m. The measured output y meas  may be based on the plant measured matrix C p meas . The matrix C meas  may represent a measured output matrix and may be based on the identity matrix I m×m  and the plant measured matrix C p meas . In the illustrated example of block  440 , the variable x represents a state vector of the vehicle based on the output observation error e yI  and the state vector of the vehicle plant x p  (e.g., the state vector of the vehicle). As represented in block  440 , the measured output y meas  is based on the measured output matrix C meas  and the state vector x. 
     In the illustrated example of block  430 , the variables A, B, and B cmd  represent the state matrix of the vehicle, the input matrix of the vehicle, and the gain command matrix of the vehicle, respectively. The variables A, B, and B cmd  are represented by the equations described in block  450 . In this example, the state matrix A is based on the variables 0 m×m , 0 n     p     ×m , C p reg , and A p . The variable 0 m×m  represents a zero matrix of size m×m, the variable 0 n     p     ×m  represents a zero matrix of size n p ×m, the variable C p reg  represents a regulated output matrix of the vehicle plant, and the variable A p  represents the state matrix of the vehicle plant. In the illustrated example, the input matrix B is based on D p reg  and B p . The variable D p reg  represents a regulated feedforward matrix of the vehicle plant, and the variable B p  represents an input matrix of the vehicle plant. In the illustrated example, the gain command matrix B cmd  is based on the variables −I m×m  and the variable 0 n     p     ×m . The variable −I m×m  represents a negative identity matrix of size m×m and the variable 0 n     p     ×m  represents a zero matrix of size n p ×m. 
     In the illustrated example of  FIG. 4 , the third vehicle controller  400  includes the vehicle plant (sI n     p     ×n     p   −A p ) −1 B p  to represent the vehicle, such as the aircraft  100 . For example, the vehicle plant may represent an air-based vehicle (e.g., the aircraft  100 , a UAV, etc.), a land-based vehicle (e.g., an automobile, a bus, a train, etc.), a marine vehicle (e.g., a boat, a submarine), etc. In some examples, the vehicle plant is a portion or represents one or more components of the vehicle. For example, the vehicle plant may be representative of one or more control surfaces operatively coupled to one of the wings  104 ,  106  of the aircraft  100 , an actuator operatively coupled to a valve of a marine vehicle, etc. In this example, the variable I n     p     ×n     p    represents an identity matrix of size n p ×n p . The designator p in the baseline control module  420  variables correspond to the plant. For example, the variable A p  represents a state matrix of the vehicle plant, the variable B p  represents an input matrix of the vehicle plant, the variable x p  represents a state of the vehicle plant, the variable I n     p     ×n     p    represents an identity matrix of the vehicle plant, etc. In the illustrated example, the variable C p reg  represents a regulated output matrix of the vehicle plant, the variable D p reg  represents a regulated feedforward matrix of the vehicle plant, and the variable C p meas  represents a measured output matrix of the vehicle plant. 
     In the illustrated example of  FIG. 4 , the third vehicle controller  400  utilizes the observer module  410  to determine the estimate of the state vector {circumflex over (x)} of an observer model based on the bounded command y cmd . In some examples, the observer module  410  may improve the estimating functions of the observer module  410  (e.g., determining the estimate of the state vector {circumflex over (x)}) by determining the output observation error e yI . In some examples, the observer module  410  may improve the estimating functions of the observer module  410  by obtaining the measured plant output y p meas  from the baseline control module  420 . In some examples, the observer module  410  obtains the measured plant output y p meas  from a collection module (e.g., the collection module  370  of  FIG. 3 ), a sensor (e.g., one(s) of the sensors  138 ,  140 ,  142 ,  144  of  FIG. 1 , the sensor(s)  350  of  FIG. 3 , etc.), etc. 
       FIG. 5  is a block diagram of an example implementation of a fourth example vehicle controller  500  that performs, executes, and/or otherwise effectuates flight control of an air-based vehicle, such as the aircraft  100  of  FIG. 1 . In some examples, the fourth vehicle controller  500  implements the first vehicle controller  102  of  FIG. 1 , the second vehicle controller  300  of  FIG. 3 , and/or the third vehicle controller  400  of  FIG. 4 . In the illustrated example of  FIG. 5 , the fourth vehicle controller  500  includes an example observer module  510  and an example baseline control module  530 . In some examples, the observer module  510  may implement the observer module  320  of  FIG. 3  and/or the observer module  410  of  FIG. 4 . In some examples, the baseline control module  530  may implement the baseline control module  330  of  FIG. 3  and/or the baseline control module  420  of  FIG. 4 . Additionally or alternatively, the fourth vehicle controller  500  may include one(s) of the command input module  310 , the observer module  320  (e.g. to implement a dual-observer model of the aircraft  100 ), the vehicle module  340 , the sensor(s)  350 , the network  360 , the collection module  370 , the datastore  380 , and/or the error module  390   FIG. 3 . 
     In the illustrated example of  FIG. 5 , the fourth vehicle controller  500  performs control of aircraft altitude in the flare regime  220  of the flight plan  202  of  FIG. 2 . For example, during the flare regime  220 , the fourth vehicle controller  500  may control the aircraft  100  from an approach glide path (e.g., the preflare aircraft flight path  210  of  FIG. 2 ) to a smooth touchdown at a desired location (e.g., at the touchdown location  214  within the touchdown zone  216 ) and at a desired sink rate (e.g., an altitude rate). 
     In the illustrated example of  FIG. 5 , the fourth vehicle controller  500  determines an estimate of a state of the altitude ĥ based on an altitude command h cmd . For example, the altitude command h cmd  may implement and/or otherwise correspond to a trajectory of the aircraft  100 . For example, the trajectory may correspond to a trajectory from a current setpoint of the aircraft  100  to the touchdown location  214  as a function of time. In this example, the baseline control module  530 , and/or, more generally, the fourth vehicle controller  500 , determines an altitude command output h based on an altitude control input δ e . For example, the altitude command output h may implement a regulated output at a specified point during the flight plan  202  that the fourth vehicle controller  500  causes the aircraft  100  to follow at a specified time. In some examples, the altitude command h cmd  is a bounded altitude command. 
     In some examples, the altitude control input δ e  implements a control surface command for a control surface of the aircraft  100 . For example, the observer module  510 , and/or, more generally, the fourth vehicle controller  500 , may generate the altitude control input δ e  to control one(s) of the elevators  130 ,  132  of  FIG. 1 . In some examples, the observer module  510  may generate the altitude control input δ e  to cause the first elevator  130  and/or the second elevator  132  to move from a first position to a second position (e.g., move up or down by one or more degrees, radians, etc.). 
     In the illustrated example of  FIG. 5 , the observer module  510  includes a gain command value B cmd    512 , a transfer function  514  of the observer model (sI n×n −A obs ) −1  (e.g. a dynamic compensator), a LQR constant gain K lqr    516 , and an observer error feedback gain L v    518 . In this example, adder logic  520  determines input(s) to the transfer function  514  based on a sum of the gain command value  512  and the observer error feedback gain  518 . In some examples, the gain command value  512  is determined based on value(s) of parameter(s) of the aircraft  100 . For example, the observer module  510  may map one or more values of parameters to the gain command value  512  in a look-up table. In some examples, the observer module  510  may map at least one of a value of a speed parameter (e.g., an airspeed parameter) of the aircraft  100 , a value of an altitude of the aircraft  100 , or a value of a configuration (e.g., a length, a width, a weight, etc.) of the aircraft  100  to a look-up table to identify the gain command value  512 . In some examples, the look-up table is stored in the datastore  380  of  FIG. 3 . 
     In some examples, the LQR constant gain  516  is determined based on value(s) of parameter(s) of the aircraft  100 . For example, the observer module  510  may map one or more values of parameters to the LQR constant gain  516  in a look-up table. In some examples, the observer module  510  may map at least one of a value of a speed parameter (e.g., an airspeed parameter) of the aircraft  100 , a value of an altitude of the aircraft  100 , or a value of a configuration (e.g., a length, a width, a weight, etc.) of the aircraft  100  to a look-up table to identify the LQR constant gain  516 . In some examples, the look-up table is stored in the datastore  380  of  FIG. 3 . 
     In some examples, A obs  is defined as a matrix (e.g., a 5×5 matrix or a matrix of any other size). In some such examples, the observer module  510  identifies values of the matrix based on flight conditions of the aircraft  100 , such as value(s) of parameters of the aircraft  100 . For example, the observer module  510  may map at least one of a value of a speed parameter (e.g., an airspeed parameter) of the aircraft  100 , a value of an altitude of the aircraft  100 , or a value of a configuration (e.g., a length, a width, a weight, etc.) of the aircraft  100  to one or more look-up tables (e.g., one or more look-up tables stored in the datastore  380  of  FIG. 3 ). In some examples, the observer module  510  may determine one or more values of the matrix based on the mapping. For example, the observer module  510  may determine A obs  based on value(s) of parameter(s) of the aircraft  100 . 
     In this example, the variable e hI  represents an output observation error based on a difference of the variables h and k cmd  applied to an integrator transfer function 1/s  622 . In this example, the difference is determined by subtraction logic  524 . In the illustrated example, the variable ê hI  represents an estimate of the output observation error e hI  and the variables ({circumflex over ({dot over (h)})}, {circumflex over (q)}, {circumflex over (θ)}) represent estimates of parameters of aircraft altitude rate {circumflex over ({dot over (h)})}, pitch rate {circumflex over (q)}, and pitch angle {circumflex over (θ)}, respectively. For example, the observer module  510  may implement a filter of sensed or measured values of the aircraft altitude rate {dot over (h)}, pitch rate q, and pitch angle θ parameters to yield and/or otherwise determine the estimates of the parameters ({circumflex over ({dot over (h)})}, {circumflex over (q)}, {circumflex over (θ)}). 
     In the illustrated example of  FIG. 5 , the baseline control module  530  implements plant dynamics (e.g., aircraft longitudinal dynamics associated with the aircraft  100 ). For example, the baseline control module  530  includes an aircraft plant (sI n     p     ×n     p   −A p ) −1 B p    532 , which represents a linear representation of the plant dynamics of the aircraft  100 . In this example, the designator p utilized in the baseline control module  530  represents the plant dynamics. For example, the variable A p  represents a state matrix of the plant dynamics and the variable B p  represents an input matrix of the plant dynamics. 
     In some examples, the aircraft altitude rate {dot over (h)}, the pitch rate q, and the pitch angle θ may be determined based on measurement(s) from sensor(s), such as one(s) of the sensors  138 ,  140 ,  142 ,  144  of  FIG. 1 , the sensor(s)  350  of  FIG. 3 , etc. For example, the baseline control module  530  may invoke the plant dynamics to determine an elevator angle associated with one(s) of the elevators  130 ,  132  of  FIG. 1 . In some examples, the baseline control module  530  may determine the elevator angle based on a measurement from a position sensor (e.g., the third sensor  142  of  FIG. 1 ) monitoring the first elevator  130 . In some examples, the baseline control module  530  may determine a thrust of the aircraft  100  based on a thrust generated by the engines  110 ,  112  of  FIG. 1 . For example, the baseline control module  530  may determine the thrust based on a measurement from a pressure sensor, a temperature, etc., and/or a combination thereof (e.g., the second sensor  140  of  FIG. 1 ). 
     In some examples, the baseline control module  530  may invoke the plant dynamics to determine aircraft altitude rate {dot over (h)} based on the elevator angle and/or the thrust. In some examples, the baseline control module  530  may invoke the plant dynamics to determine the pitch rate q based on the elevator angle and/or the thrust. In some examples, the baseline control module  530  may invoke the plant dynamics to determine the pitch angle θ based on the elevator angle. 
     In example operation, the fourth vehicle controller  500  may perform observer-based landing control of the aircraft  100 . For example, the observer module  510  may execute the transfer function  514  to determine first states, such as estimates of the output observation error ê hI , the aircraft altitude rate {circumflex over ({dot over (h)})}, the pitch rate {circumflex over (q)}, the pitch angle {circumflex over (θ)}, and the altitude ĥ. In example operation, the observer module  510  applies the LQR constant gain  516  to the first states to determine the altitude control input δ e . 
     In example operation, the baseline control module  530  may execute the aircraft plant  532  to determine second states, such as measured, sensed, and/or otherwise known values of the aircraft altitude rate {dot over (h)}, the pitch rate q, the pitch angle θ, and the altitude h. For example, the baseline control module  530  may determine the second states of the aircraft  100  based on the aircraft  100  executing the altitude control input δ e . For example, the fourth vehicle controller  500  may determine the second states based on the elevators  130 ,  132  of  FIG. 1  moving and/or otherwise actuating based on the altitude control input δ e . 
     In example operation, the observer module  510  may transpose the measured aircraft altitude rate {dot over (h)}, pitch rate q, pitch angle θ, and altitude h along with the output observation error e hI . The observer module  510  may apply the observer error feedback gain  518  to the transposed one(s) of the measured aircraft altitude rate {dot over (h)}, pitch rate q, pitch angle θ, altitude h, and output observation error e hI . The adder logic  520  may add the output(s) of such an operation and the gain command value  512  to determine the input(s) to the transfer function  514 . 
     In example operation, the fourth vehicle controller  500  may determine third states, such as new or updated estimate of the first states, based on the difference between the altitude command h cmd  and the altitude command output h. For example, the subtraction logic  524  may determine the difference between the altitude command h cmd  and the altitude command output h, which may be used to determine the output observation error e hI . The observer module  510  may use the output observation error e hI  to determine the third states, such as new or updated values of the estimates of the output observation error ê hI , the aircraft altitude rate {circumflex over ({dot over (h)})}, the pitch rate {circumflex over (q)}, the pitch angle {circumflex over (θ)}, and the altitude ĥ, using the transfer function  514 . Advantageously, the observer module  510  may determine and/or generate an updated altitude control input δ e  to control one or more flight control surfaces of the aircraft  100  during the flare regime  220 , such as one(s) of the elevators  130 ,  132  based on the difference between the first states and the second states. 
     While an example manner of implementing the first vehicle controller  102  of  FIG. 1 , the second vehicle controller  300  of  FIG. 3 , the third vehicle controller  400  of  FIG. 4 , and/or fourth vehicle controller  500  of  FIG. 5  in depicted in  FIGS. 3, 4 , and/or  5 , one or more of the elements, processes, and/or devices illustrated in  FIGS. 3, 4 , and/or  5  may be combined, divided, re-arranged, omitted, eliminated, and/or implemented in any other way. Further, one(s) of the example command input module  310 , the example observer module  320 , the example baseline control module  330 , the example vehicle module  340 , the example sensor(s)  350 , the example network  360 , the example collection module  370 , the example datastore  380 , and/or the example error module  390  of  FIG. 3 , one(s) of the example observer module  410  and/or the example baseline control module  420  of  FIG. 4 , and/or one(s) of the example observer module  510 , the example gain command value  512 , the example transfer function  514 , the example LQR constant gain  516 , the example error observer feedback gain  518 , the example adder logic  520 , the example integrator transfer function  522 , the example subtraction logic  524 , the example baseline control module  530 , and/or the example aircraft plant  532  of  FIG. 5 , and/or, more generally, one(s) of the first example vehicle controller  102 , the second example vehicle controller  300 , the third example vehicle controller  400 , and/or the fourth example vehicle controller  500 , may be implemented by hardware, software, firmware and/or any combination of hardware, software and/or firmware. Thus, for example, any of the example command input module  310 , the example observer module  320 , the example baseline control module  330 , the example vehicle module  340 , the example sensor(s)  350 , the example network  360 , the example collection module  370 , the example datastore  380 , the example error module  390 , the example observer module  410 , the example baseline control module  420 , the example observer module  510 , the example gain command value  512 , the example transfer function  514 , the example LQR constant gain  516 , the example error observer feedback gain  518 , the example adder logic  520 , the example integrator transfer function  522 , the example subtraction logic  524 , the example baseline control module  530 , the example aircraft plant  532 , and/or, more generally, the first example vehicle controller  102 , the second example vehicle controller  300 , the third example vehicle controller  400 , and/or the fourth example vehicle controller  500  could be implemented by one or more analog or digital circuit(s), logic circuits, programmable processor(s), application specific integrated circuit(s) (ASIC(s)), programmable logic device(s) (PLD(s)), and/or field programmable logic device(s) (FPLD(s)) (e.g., field programmable gate array (FPGA) device(s) (FPGA(s))). When reading any of the apparatus or system claims of this patent to cover a purely software and/or firmware implementation, at least one of the example command input module  310 , the example observer module  320 , the example baseline control module  330 , the example vehicle module  340 , the example sensor(s)  350 , the example network  360 , the example collection module  370 , the example datastore  380 , the example error module  390 , the example observer module  410 , the example baseline control module  420 , the example observer module  510 , the example gain command value  512 , the example transfer function  514 , the example LQR constant gain  516 , the example error observer feedback gain  518 , the example adder logic  520 , the example integrator transfer function  522 , the example subtraction logic  524 , the example baseline control module  530 , the example aircraft plant  532 , and/or, more generally, the first example vehicle controller  102 , the second example vehicle controller  300 , the third example vehicle controller  400 , and/or the fourth example vehicle controller  500  is/are hereby expressly defined to include a tangible computer readable storage device or storage disk such as a memory, a DVD, a CD, a Blu-ray disk, etc., storing the software and/or firmware. Further still, the first example vehicle controller  102 , the second example vehicle controller  300 , the third example vehicle controller  400 , and/or the fourth example vehicle controller  500  may include one or more elements, processes, and/or devices in addition to, or instead of, those illustrated in  FIGS. 3, 4 , and/or  5 , and/or may include more than one of any or all of the illustrated elements, processes, and devices. 
     Flowcharts representative of example hardware logic, machine readable instructions, hardware implemented state machines, and/or any combination thereof for implementing the first example vehicle controller  102  of  FIG. 1 , the second example vehicle controller  300  of  FIG. 3 , the third example vehicle controller  400  of  FIG. 4 , and/or the fourth example vehicle controller  500  of  FIG. 5  are shown in  FIGS. 6-9 . The machine readable instructions may be one or more executable programs or portion(s) of an executable program for execution by a computer processor and/or processor circuitry, such as the processor  1012  shown in the example processor platform  1000  discussed below in connection with  FIG. 10 . The program may be embodied in software stored on a non-transitory computer readable storage medium such as a CD-ROM, a floppy disk, a hard drive, a DVD, a Blu-ray disk, or a memory associated with the processor  1012 , but the entire program and/or parts thereof could alternatively be executed by a device other than the processor  1012  and/or embodied in firmware or dedicated hardware. Further, although the example program is described with reference to the flowcharts illustrated in  FIGS. 6-9 , many other methods of implementing the first vehicle controller  102  of  FIG. 1 , the second vehicle controller  300  of  FIG. 3 , the third vehicle controller  400  of  FIG. 4 , and/or the fourth vehicle controller  500  of  FIG. 5  may alternatively be used. For example, the order of execution of the blocks may be changed, and/or some of the blocks described may be changed, eliminated, or combined. Additionally or alternatively, any or all of the blocks may be implemented by one or more hardware circuits (e.g., discrete and/or integrated analog and/or digital circuitry, an FPGA, an ASIC, a comparator, an operational-amplifier (op-amp), a logic circuit, etc.) structured to perform the corresponding operation without executing software or firmware. The processor circuitry may be distributed in different network locations and/or local to one or more devices (e.g., a multi-core processor in a single machine, multiple processors distributed across a server rack, etc.). 
     The machine readable instructions described herein may be stored in one or more of a compressed format, an encrypted format, a fragmented format, a compiled format, an executable format, a packaged format, etc. Machine readable instructions as described herein may be stored as data or a data structure (e.g., portions of instructions, code, representations of code, etc.) that may be utilized to create, manufacture, and/or produce machine executable instructions. For example, the machine readable instructions may be fragmented and stored on one or more storage devices and/or computing devices (e.g., servers) located at the same or different locations of a network or collection of networks (e.g., one or more networks of a vehicle). The machine readable instructions may require one or more of installation, modification, adaptation, updating, combining, supplementing, configuring, decryption, decompression, unpacking, distribution, reassignment, compilation, etc. in order to make them directly readable, interpretable, and/or executable by a computing device and/or other machine. For example, the machine readable instructions may be stored in multiple parts, which are individually compressed, encrypted, and stored on separate computing devices, wherein the parts when decrypted, decompressed, and combined form a set of executable instructions that implement one or more functions that may together form a program such as that described herein. 
     In another example, the machine readable instructions may be stored in a state in which they may be read by processor circuitry, but require addition of a library (e.g., a dynamic link library (DLL)), a software development kit (SDK), an application programming interface (API), etc., in order to execute the instructions on a particular computing device or other device. In another example, the machine readable instructions may need to be configured (e.g., settings stored, data input, network addresses recorded, etc.) before the machine readable instructions and/or the corresponding program(s) can be executed in whole or in part. Thus, machine readable media, as used herein, may include machine readable instructions and/or program(s) regardless of the particular format or state of the machine readable instructions and/or program(s) when stored or otherwise at rest or in transit. 
     The machine readable instructions described herein can be represented by any past, present, or future instruction language, scripting language, programming language, etc. For example, the machine readable instructions may be represented using any of the following languages: C, C++, Java, C#, Perl, Python, JavaScript, HyperText Markup Language (HTML), Structured Query Language (SQL), Swift, etc. 
     As mentioned above, the example processes of  FIGS. 6-9  may be implemented using executable instructions (e.g., computer and/or machine readable instructions) stored on a non-transitory computer and/or machine readable medium such as a hard disk drive, a flash memory, a read-only memory, a compact disk, a DVD, a cache, a random-access memory, and/or any other storage device or storage disk in which information is stored for any duration (e.g., for extended time periods, permanently, for brief instances, for temporarily buffering, and/or for caching of the information). As used herein, the term non-transitory computer readable medium is expressly defined to include any type of computer readable storage device and/or storage disk and to exclude propagating signals and to exclude transmission media. 
     “Including” and “comprising” (and all forms and tenses thereof) are used herein to be open ended terms. Thus, whenever a claim employs any form of “include” or “comprise” (e.g., comprises, includes, comprising, including, having, etc.) as a preamble or within a claim recitation of any kind, it is to be understood that additional elements, terms, etc. may be present without falling outside the scope of the corresponding claim or recitation. As used herein, when the phrase “at least” is used as the transition term in, for example, a preamble of a claim, it is open-ended in the same manner as the term “comprising” and “including” are open ended. The term “and/or” when used, for example, in a form such as A, B, and/or C refers to any combination or subset of A, B, C such as (1) A alone, (2) B alone, (3) C alone, (4) A with B, (5) A with C, (6) B with C, and (7) A with B and with C. As used herein in the context of describing structures, components, items, objects and/or things, the phrase “at least one of A and B” is intended to refer to implementations including any of (1) at least one A, (2) at least one B, and (3) at least one A and at least one B. Similarly, as used herein in the context of describing structures, components, items, objects and/or things, the phrase “at least one of A or B” is intended to refer to implementations including any of (1) at least one A, (2) at least one B, and (3) at least one A and at least one B. As used herein in the context of describing the performance or execution of processes, instructions, actions, activities and/or steps, the phrase “at least one of A and B” is intended to refer to implementations including any of (1) at least one A, (2) at least one B, and (3) at least one A and at least one B. Similarly, as used herein in the context of describing the performance or execution of processes, instructions, actions, activities and/or steps, the phrase “at least one of A or B” is intended to refer to implementations including any of (1) at least one A, (2) at least one B, and (3) at least one A and at least one B. 
     As used herein, singular references (e.g., “a”, “an”, “first”, “second”, etc.) do not exclude a plurality. The term “a” or “an” entity, as used herein, refers to one or more of that entity. The terms “a” (or “an”), “one or more”, and “at least one” can be used interchangeably herein. Furthermore, although individually listed, a plurality of means, elements or method actions may be implemented by, e.g., a single unit or processor. Additionally, although individual features may be included in different examples or claims, these may possibly be combined, and the inclusion in different examples or claims does not imply that a combination of features is not feasible and/or advantageous. 
       FIG. 6  is a flowchart representative of example machine readable instructions  600  that may be executed to implement the first vehicle controller  102  of  FIG. 1 , the second vehicle controller  300  of  FIG. 3 , the third vehicle controller  400  of  FIG. 4 , and/or the fourth vehicle controller  500  of  FIG. 5  to perform observer-based landing control of the aircraft  100  of  FIGS. 1 and/or 2 . The example machine readable instructions  600  begin at block  602 , at which the vehicle controller  102 ,  300 ,  400 ,  500  generates a command input. For example, the command input module  310  ( FIG. 3 ) may generate a command input for the aircraft  100  based on pilot or unmanned control input (e.g., a command from a pilot, a computing device controlled by the pilot, a UAV computing device, etc.), a value from the datastore  380  ( FIG. 3 ), measurement(s) from the sensor(s)  350  ( FIG. 3 ) obtained from the collection module  370  ( FIG. 3 ), a guidance module, etc. 
     At block  604 , the vehicle controller  102 ,  300 ,  400 ,  500  determines a current state of a vehicle parameter. For example, the observer module  320  ( FIG. 3 ), the observer module  410  ( FIG. 4 ), and/or the observer module  510  ( FIG. 5 ) may determine an initial state of an angle of attack parameter of the aircraft. 
     At block  606 , the vehicle controller  102 ,  300 ,  400 ,  500  determines an estimate of a state of the vehicle parameter. For example, the observer module  320 ,  410 ,  510  may determine an estimate of the state of the angle of attack parameter of the aircraft  100  based on one or more observer models of the aircraft  100 . 
     At block  608 , the vehicle controller  102 ,  300 ,  400 ,  500  generates a baseline command. For example, the baseline control module  330  ( FIG. 3 ), the baseline control module  420  ( FIG. 4 ), and/or the baseline control module  530  ( FIG. 5 ) may generate a baseline command for the aircraft  100  based on the estimate of the state of the angle of attack parameter of the aircraft  100 . 
     At block  610 , the vehicle controller  102 ,  300 ,  400 ,  500  determines the control input. For example, the baseline control module  330 ,  420 ,  530  may determine the control input (e.g., the control input u) based on the guidance command (e.g., the guidance command r) and/or the estimate of the state of the angle of attack parameter for the aircraft. 
     At block  612 , the vehicle controller  102 ,  300 ,  400 ,  500  executes a command. For example, the vehicle module  340  ( FIG. 3 ) may execute the command based on the control input (e.g., the control input u). 
     At block  614 , the vehicle controller  102 ,  300 ,  400 ,  500  measures a state of the vehicle parameter. For example, the collection module  370  ( FIG. 3 ) may measure the state of the angle of attack parameter based on a measurement from the sensor(s)  350  ( FIG. 3 ). In some examples, the observer module  320 ,  410 ,  510  may measure the state of the angle of attack parameter based on the measurement from the sensor(s)  350 . 
     At block  616 , the vehicle controller  102 ,  300 ,  400 ,  500  determines a difference between the measured state and the estimate of the state. For example, the error module  390  may determine the difference between (1) the measured state of the angle of attack parameter based on the measurement from the sensor(s)  350  and (2) the estimate of the state of the angle of attack parameter determined by the observer module  320 ,  410 ,  510 . 
     At block  618 , the vehicle controller  102 ,  300 ,  400 ,  500  determines whether the difference satisfies a threshold. For example, the observer module  320 ,  410 ,  510  may determine whether the difference satisfies an estimation error threshold (e.g., a threshold indicating the difference is greater than 5 degrees, the difference is less than 10 radians/second, etc.). In some examples, the observer module  320 ,  410 ,  510  may output an updated estimate of the state of the angle of attack parameter based on the difference to improve control of the aircraft  100  based on the updated estimate. 
     If, at block  618 , the vehicle controller  102 ,  300 ,  400 ,  500  determines that the difference does not satisfy the threshold, control returns to block  602  to generate another guidance command, otherwise the example machine readable instructions  600  of  FIG. 6  concludes. 
       FIG. 7  is a flowchart representative of example machine readable instructions  700  that may be executed to implement the first vehicle controller  102  of  FIG. 1 , the second vehicle controller  300  of  FIG. 3 , the third vehicle controller  400  of  FIG. 4 , and/or the fourth vehicle controller  500  of  FIG. 5  to perform observer-based landing control of the aircraft  100  of  FIGS. 1 and/or 2 . The example machine readable instructions  700  begin at block  702 , at which the vehicle controller  102 ,  300 ,  400 ,  500  determines a regime of a flight plan of an aircraft. For example, the fourth vehicle controller  500  may determine that the aircraft  100  has achieved the flare engage altitude at the second waypoint  208  ( FIG. 2 ) at a beginning of the flare regime  220  ( FIG. 2 ). In some examples, the fourth vehicle controller  500  determines the regime of the flight plan  202  ( FIG. 2 ) to be the flare regime  220  based on the altitude command h cmd . In some examples, the fourth vehicle controller  500  determines the regime of the flight plan  202  to be the flare regime  220  based on measurement(s) from the sensor(s)  350  (e.g., an altitude measurement from an altimeter), a command from the vehicle module  340  ( FIG. 3 ), etc. For example, the vehicle module  340  may determine that the regime of the flight plan  202  is the flare regime  220  based on pilot input or unmanned pilot input. 
     At block  704 , the vehicle controller  102 ,  300 ,  400 ,  500  determines whether the regime is the flare regime. For example, the fourth vehicle controller  500  may not control the aircraft  100  in response to determining that the regime of the flight plan  202  is not the flare regime  220 . In such examples, a different aircraft control system (e.g., a non-observer model based aircraft control system) of the aircraft  100  may control the aircraft during other regimes of the flight plan  202 . 
     If, at block  704 , the vehicle controller  102 ,  300 ,  400 ,  500  determines that the regime is not the flare regime, control proceeds to block  706  to execute non-observer based aircraft control. For example, the aircraft  100  may be controlled by a non-observer model based aircraft control system. In some examples, the aircraft  100  may be controlled by portion(s) of the second vehicle controller  300  ( FIG. 3 ). For example, the aircraft  100  may be controlled by at least one of the command input module  310 , the baseline control module  330 , the vehicle module  340 , the sensor(s)  350 , the network  360 , the collection module  370 , or the datastore  380 . In such examples, the observer module  320  may be disabled when the regime of the flight plan  202  is not the flare regime  220 . In response to executing non-observer based aircraft control at block  706 , control proceeds to block  722  to determine whether to continue monitoring the aircraft. 
     If, at block  704 , the vehicle controller  102 ,  300 ,  400 ,  500  determines that the regime is the flare regime, control proceeds to block  708  to enable observer-based landing control. For example, the fourth vehicle controller  500  may enable at least one of the observer module  510  or the baseline control module  530  to be enabled to land (e.g., automatically land) the aircraft  100  during the flare regime  220  of the flight plan  202 . In some examples, the fourth vehicle controller  500  may enable at least one of the observer module  510  or the baseline control module  530  in response to determining the regime to be the flare regime  220 , a pilot input or unmanned pilot input, measurement(s) from one(s) of the sensors  138 ,  140 ,  142 ,  144  of  FIG. 1 , etc., and/or a combination thereof. 
     At block  710 , the vehicle controller  102 ,  300 ,  400 ,  500  determines an altitude command. For example, the fourth vehicle controller  500  may determine the altitude command h cmd . In some examples, the fourth vehicle controller  500  determines the altitude command h cmd  based on a command, instruction, etc., from the command input module  310  ( FIG. 3 ), measurement(s) from the sensor(s)  350  ( FIG. 3 ), a command, instruction, etc., from the datastore  380  ( FIG. 3 ), etc., and/or a combination thereof. For example, the observer module  510  may obtain the altitude command h cmd  from the command input module  310 , the datastore  380 , and/or other portion(s) of the first vehicle controller  102 , the second vehicle controller  300 , etc. 
     At block  712 , the vehicle controller  102 ,  300 ,  400 ,  500  determines an estimate state of an aircraft parameter, such as an altitude of the aircraft  100 , based on a transfer function of an observer model. For example, the observer module  510  ( FIG. 5 ) may invoke and/or otherwise cause an execution of the transfer function  514  to determine {circumflex over ({dot over (h)})}, {circumflex over (q)}, {circumflex over (θ)}, and ĥ, which are estimates of the aircraft altitude rate, the pitch rate, the pitch angle, and the altitude, respectively. In such examples, the observer module  510  may execute the transfer function based on the altitude command h cmd . 
     At block  714 , the vehicle controller  102 ,  300 ,  400 ,  500  determines an altitude control input based on the estimate states. For example, the observer module  510  may determine the altitude control input δ e  based on the LQR constant gain K lqr    616  and the estimates of the aircraft altitude rate, the pitch rate, the pitch angle, and the altitude. 
     At block  716 , the vehicle controller  102 ,  300 ,  400 ,  500  determines an altitude command output based on the altitude control input and an aircraft plant. For example, the baseline control module  530  may determine the altitude command output h by invoking the longitudinal dynamics represented by the aircraft plant  532  based on the altitude control input δ e  determined by the observer module  510 . 
     At block  718 , the vehicle controller  102 ,  300 ,  400 ,  500  control elevator(s) of the aircraft  100  based on the altitude command output. For example, the baseline control module  530  may output the altitude command output h to facilitate control of one(s) of the elevators  130 ,  132  ( FIG. 1 ). In some examples, the baseline control module  530  provides the altitude command output h to the first actuator  148  to control the first elevator  130  to move from a first position to a second position. In some examples, the baseline control module  530  provides the altitude command output h to the vehicle module  340  ( FIG. 3 ), which may provide the altitude command output h to the first actuator  148  to control the first elevator  130  to move from a first position to a second position. 
     At block  720 , the vehicle controller  102 ,  300 ,  400 ,  500  determines measured state(s) of the aircraft parameter(s) in response to the control of the elevator(s). For example, in response to the elevators  130 ,  132 , and/or, more generally, the aircraft  100 , operating based on the altitude command output h, the baseline control module  530  may determine {dot over (h)}, q, θ, and h, which are measured states of the aircraft altitude rate {dot over (h)}, the pitch rate q, the pitch angle θ, and the altitude h, respectively. In some examples, the baseline control module  530  may determine such measured states based on measurement(s) from one(s) of the sensors  138 ,  140 ,  142 ,  144  of  FIG. 1 . For example, the observer module  510  may determine updated estimates of {circumflex over ({dot over (h)})}, {circumflex over (q)}, {circumflex over (θ)}, and ĥ based on a difference between the altitude command h cmd  and the altitude command output h. 
     At block  722 , the vehicle controller  102 ,  300 ,  400 ,  500  determines whether to continue monitoring the aircraft. For example, the observer module  510 , and/or, more generally, the fourth vehicle controller  500 , may determine to continue controlling the landing of the aircraft  100  because the aircraft  100  is in the flare regime  220  of the flight plan  202 . In some examples, the observer module  510 , and/or, more generally, the fourth vehicle controller  500  may determine to not continue controlling the landing of the aircraft  100  because the aircraft  100  landed at the touchdown location  214  ( FIG. 2 ). 
     If, at block  722 , the vehicle controller  102 ,  300 ,  400 ,  500  determines to continue monitoring the aircraft, control returns to block  702  to determine the regime of the flight plan of the aircraft  100 . If, at block  722 , the vehicle controller  102 ,  300 ,  400 ,  500  determines not to continue monitoring the aircraft, the example machine readable instructions  700  of  FIG. 7  conclude. 
       FIG. 8  is a flowchart representative of example machine readable instructions  800  that may be executed to implement the first vehicle controller  102  of  FIG. 1 , the second vehicle controller  300  of  FIG. 3 , the third vehicle controller  400  of  FIG. 4 , and/or the fourth vehicle controller  500  of  FIG. 5  to perform observer-based landing control of the aircraft  100  of  FIGS. 1 and/or 2 . The example machine readable instructions  800  begin at block  802 , at which the vehicle controller  102 ,  300 ,  400 ,  500  determines an altitude command of an aircraft in a flare regime of a flight plan. For example, the fourth vehicle controller  500  may determine the altitude command h cmd . In some examples, the fourth vehicle controller  500  determines the altitude command h cmd  based on a command, instruction, etc., from the command input module  310  ( FIG. 3 ), measurement(s) from the sensor(s)  350  ( FIG. 3 ), a command, instruction, etc., from the datastore  380  ( FIG. 3 ), etc., and/or a combination thereof. For example, the observer module  510  ( FIG. 5 ) may obtain the altitude command h cmd  from the command input module  310 , the datastore  380 , and/or other portion(s) of the first vehicle controller  102 , the second vehicle controller  300 , etc. 
     At block  804 , the vehicle controller  102 ,  300 ,  400 ,  500  determines inputs to an observer transfer function based on the altitude command and the measured states. For example, the observer module  510  may determine one or more inputs to the transfer function  514  ( FIG. 5 ) including the gain command value  512 . An example process that may be executed to implement block  804  is described below in connection with  FIG. 10 . 
     At block  806 , the vehicle controller  102 ,  300 ,  400 ,  500  determines an observer matrix based on a flight conditions matrix associated with sensor measurement(s). For example, the observer module  510  may determine A obs  based on a matrix including values for one or more flight conditions associated with measurement(s) from one(s) of the sensors  138 ,  140 ,  142 ,  144  of  FIG. 1 . In some examples, the observer module  510  may map a first flight condition of an airspeed of the aircraft  100  based on a measurement from the first sensor  138  or a different sensor, a second flight condition of an altitude of the aircraft  100  based on a measurement from the first sensor  138  or a different sensor, a third flight condition of a weight of the aircraft  100  based on a measurement from a sensor that may be monitoring fuel capacity of the aircraft  100 , etc., to one or more values in a look-up table. For example, the observer module  510  may map the first flight condition, the second flight condition, the third flight condition, etc., to the one or more values to populate and/or otherwise generate A obs  of the transfer function  514 . 
     At block  808 , the vehicle controller  102 ,  300 ,  400 ,  500  executes the observer transfer function based on a difference between an identity matrix and the observer matrix to output a state matrix. For example, the observer module  510  may execute the transfer function  514  based on a difference between the term sI n×n , which is based on the identity matrix I n×n , and A obs , to determine the output state matrix including the terms ê hI , {circumflex over ({dot over (h)})}, {circumflex over (q)}, {circumflex over (θ)}, and ĥ, which represent estimates of parameters of the aircraft  100 . 
     At block  810 , the vehicle controller  102 ,  300 ,  400 ,  500  determine an altitude control input based on the output state matrix. For example, the observer module  510  may determine the altitude control input δ e  based on the terms ê hI , {circumflex over ({dot over (h)})}, {circumflex over (q)}, {circumflex over (θ)}, and ĥ applied respectively to the LQR constant gain K lqr    616 . 
     At block  812 , the vehicle controller  102 ,  300 ,  400 ,  500  determines aircraft longitudinal dynamics in response to the altitude control input. For example, the baseline control module  530  may invoke the aircraft plant  532  to determine aircraft longitudinal dynamics of the aircraft  100 , which may include a first velocity of the aircraft  100  along a body axis of the aircraft  100 , a second velocity of the aircraft  100  perpendicular to the body axis of the aircraft  100 , an angle (e.g., a body angle) between the body axis and the horizontal axis of the aircraft  100 , an angular velocity of the aircraft  100 , etc., and/or a combination thereof. 
     At block  814 , the vehicle controller  102 ,  300 ,  400 ,  500  determines measured aircraft parameters based on the aircraft longitudinal dynamics. For example, the baseline control module  530  may determine measured values of aircraft parameters including an altitude, a pitch rate, a pitch angle, etc., of the aircraft  100  based on measurement(s) from one(s) of the sensors  138 ,  140 ,  142 ,  144 . In some examples, the baseline control module  530  may determine the measured values of the aircraft parameters in response to a change in the aircraft longitudinal dynamics of the aircraft  100  based on the aircraft  100  being controlled based on the altitude control input δ e . 
     At block  816 , the vehicle controller  102 ,  300 ,  400 ,  500  determines measured states and an altitude command output based on the measured aircraft parameters. For example, the baseline control module  530  may determine the measured states {dot over (h)}, q, θ, and h of  FIG. 5  in response to the aircraft  100  being controlled based on the altitude control input δ e . In some examples, the baseline control module  530  may determine and/or otherwise output the altitude command output h to control one or more flight control surfaces of the aircraft  100 , such as one(s) of the elevators  130 ,  132  of  FIG. 1 . 
     At block  818 , the vehicle controller  102 ,  300 ,  400 ,  500  calculates a difference between the altitude command and the altitude command output. For example, the subtraction logic  524  ( FIG. 5 ) may determine the difference between the altitude command h cmd  and the altitude command output h. 
     At block  820 , the vehicle controller  102 ,  300 ,  400 ,  500  determines whether the difference satisfies a threshold. For example, the subtraction logic  524  may determine that the difference between a first command (e.g., the altitude command h cmd ) to control the first elevator  130  to have an elevator angle of 30 degrees and a second command (e.g., the altitude command output h) to control the first elevator  130  to have an elevator angle of 27 degrees is 3 degrees, which may be greater than a threshold of 2 degrees and thereby satisfies the threshold. 
     If, at block  820 , the subtraction logic  524  determines that the difference does not satisfy the threshold, control returns to block  802  to determine another altitude command of the aircraft in the flare regime of the flight plan. If, at block  820 , the subtraction logic  524  determines that the difference satisfies the threshold, then, at block  822 , the vehicle controller  102 ,  300 ,  400 ,  500  generates an alert. For example, the subtraction logic  524  or a different module or logic of the fourth vehicle controller  500  may generate an alert, an indication, etc., to indicate that the difference satisfies the threshold. In some examples, the subtraction logic  524  may generate the alert by transmitting data to a user interface of the aircraft  100 , which may display the alert, the data, etc., to a pilot of the aircraft  100 . For example, the pilot may take corrective action or adjust a configuration of the aircraft  100  based on the alert. In response to generating the alert at block  822 , the machine readable instructions  800  of  FIG. 8  conclude. 
       FIG. 9  is a flowchart representative of example machine readable instructions  900  that may be executed to implement the first vehicle controller  102  of  FIG. 1 , the second vehicle controller  300  of  FIG. 3 , the third vehicle controller  400  of  FIG. 4 , and/or the fourth vehicle controller  500  of  FIG. 5  to determine inputs to an observer transfer function based an altitude command and measured states. For example, the machine readable instructions  900  of  FIG. 9  may be executed to implement block  804  of the machine readable instructions  800  of  FIG. 8 . The example machine readable instructions  900  begin at block  902 , at which the vehicle controller  102 ,  300 ,  400 ,  500  determines a gain command value. For example, the observer module  510  ( FIG. 5 ) may determine the gain command value  512  ( FIG. 5 ) based on one or more parameters of the aircraft  100 . 
     At block  904 , the vehicle controller  102 ,  300 ,  400 ,  500  determines first input(s) based on the altitude command and the gain command value. For example, the observer module  510  may determine one or more first inputs to the adder logic  520  ( FIG. 5 ) based on applying the gain command value  512  to the altitude command 
     At block  906 , the vehicle controller  102 ,  300 ,  400 ,  500  determines a configuration of the aircraft. For example, the observer module  510  may query the collection module  370  ( FIG. 3 ), the datastore  380  ( FIG. 3 ), etc., to determine a configuration of the aircraft  100 . In some examples, the configuration may include physical dimensions, specifications, etc., of the aircraft  100  such as a height, width, length, and/or weight of the aircraft  100 . 
     At block  908 , the vehicle controller  102 ,  300 ,  400 ,  500  determines an L v  constant based on a mapping of at least one of the configuration or one(s) of aircraft parameters to a look-up table. For example, the observer module  510  may determine the observer error feedback gain L v    518  based on a mapping of at least one of the configuration or one(s) of aircraft parameters (e.g., an airspeed, an altitude, etc.) of the aircraft  100  to a look-up table to identify the observer error feedback gain L v    518 . 
     At block  910 , the vehicle controller  102 ,  300 ,  400 ,  500  integrates a difference between the altitude command and an altitude command output. For example, the integrator transfer function  522  may integrate the difference between the altitude command h cmd  and the altitude command output h to determine the output observation error e hI   
     At block  912 , the vehicle controller  102 ,  300 ,  400 ,  500  determines measured states based on the measured aircraft parameters. For example, the observer module  510  may determine the measured states {dot over (h)}, q, θ, and h of  FIG. 5 . In some examples, the observer module  510  determines the measured states by transposing the measured states obtained from the baseline control module  530 . 
     At block  914 , the vehicle controller  102 ,  300 ,  400 ,  500  determines second input(s) based on at least one of the L v  constant, the measured states, or the integrated difference. For example, the observer module  510  may add the output observation error e hI  to a matrix that includes the measured states. The observer module  510  may transpose the matrix that includes the output observation error e hI  and the measured states to yield the transposed matrix (e hI  {dot over (h)} q θ h) T . The observer module  510  may apply the observer error feedback gain L v    518  to the transposed matrix to yield a scaled or adjusted transposed matrix to represent the second inputs to the adder logic  520   FIG. 5 ). 
     At block  916 , the vehicle controller  102 ,  300 ,  400 ,  500  determines the input(s) based on a sum of the first input(s) and the second input(s). For example, the adder logic  520  may determine the input(s) to the transfer function  514  based on a sum of the first inputs and the second inputs. In response to determining the input(s) based on the sum of the first input(s) and the second input(s) at block  916 , the machine readable instructions  900  of  FIG. 9  return to block  806  of the machine readable instructions  800  of  FIG. 8  to determine an observer matrix based on a flight conditions matrix associated with sensor measurement(s). Alternatively, in response to determining the input(s) based on the sum of the first input(s) and the second input(s) at block  916 , the machine readable instructions  900  of  FIG. 9  may conclude. 
       FIG. 10  is a block diagram of an example processor platform  1000  structured to execute the instructions of  FIGS. 6-9  to implement the first example vehicle controller  102 , the second example vehicle controller  300 , the third example vehicle controller  400 , and/or the fourth example vehicle controller  500  of  FIGS. 1, 2, 3, 4 , and/or  5 . The processor platform  1000  can be, for example, an aircraft computer, an industrial computer, a line replaceable unit, a remote electronic unit, a server, or any other type of computing device. 
     The processor platform  1000  of the illustrated example includes a processor  1012 . The processor  1012  of the illustrated example is hardware. For example, the processor  1012  can be implemented by one or more integrated circuits, logic circuits, microprocessors, GPUs, DSPs, or controllers from any desired family or manufacturer. The hardware processor may be a semiconductor based (e.g., silicon based) device. In this example, the processor  1012  implements the example command input module  310 , the example observer module  320 , the example baseline control module  330 , the example vehicle module  340 , the example sensor(s)  350 , the example network  360 , the example collection module  370 , the example error module  390 , the example observer module  410  of  FIG. 4 , the example baseline control module  420  of  FIG. 4 , the example observer module  510  of  FIG. 5 , the example gain command value  512 , the example transfer function  514 , the example LQR constant gain  516 , the example error observer feedback gain  518 , the example adder logic  520  of  FIG. 5 , the example integrator transfer function  522 , the example subtraction logic  524 , the example baseline control module  530  of  FIG. 5 , and the example aircraft plant  532  of  FIGS. 3, 4 , and/or  5 . 
     The processor  1012  of the illustrated example includes a local memory  1013  (e.g., a cache). The processor  1012  of the illustrated example is in communication with a main memory including a volatile memory  1014  and a non-volatile memory  1016  via a bus  1018 . The volatile memory  1014  may be implemented by Synchronous Dynamic Random Access Memory (SDRAM), Dynamic Random Access Memory (DRAM), RAMBUS® Dynamic Random Access Memory (RDRAM®) and/or any other type of random access memory device. The non-volatile memory  1016  may be implemented by flash memory and/or any other desired type of memory device. Access to the main memory  1014 ,  1016  is controlled by a memory controller. 
     The processor platform  1000  of the illustrated example also includes an interface circuit  1020 . The interface circuit  1020  may be implemented by any type of interface standard, such as an Ethernet interface, a universal serial bus (USB), a Bluetooth® interface, a near field communication (NFC) interface, and/or a PCI express interface. 
     In the illustrated example, one or more input devices  1022  are connected to the interface circuit  1020 . The input device(s)  1022  permit(s) a user to enter data and/or commands into the processor  1012 . The input device(s) can be implemented by, for example, an audio sensor, a microphone, a camera (still or video), a keyboard, a button, a mouse, a touchscreen, a track-pad, a trackball, an isopoint device, and/or a voice recognition system. 
     One or more output devices  1024  are also connected to the interface circuit  1020  of the illustrated example. The output devices  1024  can be implemented, for example, by display devices (e.g., a light emitting diode (LED), an organic light emitting diode (OLED), a liquid crystal display (LCD), a cathode ray tube (CRT) display, an in-place switching (IPS) display, a touchscreen, etc.), a tactile output device, a printer and/or speaker. The interface circuit  1020  of the illustrated example, thus, typically includes a graphics driver card, a graphics driver chip and/or a graphics driver processor. 
     The interface circuit  1020  of the illustrated example also includes a communication device such as a transmitter, a receiver, a transceiver, a modem, a residential gateway, a wireless access point, and/or a network interface to facilitate exchange of data with external machines (e.g., computing devices of any kind) via a network  1026 . The communication can be via, for example, an Ethernet connection, a digital subscriber line (DSL) connection, a telephone line connection, a coaxial cable system, a satellite system, a line-of-site wireless system, a cellular telephone system, etc. 
     The processor platform  1000  of the illustrated example also includes one or more mass storage devices  1028  for storing software and/or data. Examples of such mass storage devices  1028  include floppy disk drives, hard drive disks, compact disk drives, Blu-ray disk drives, redundant array of independent disks (RAID) systems, and digital versatile disk (DVD) drives. In this example, the one or more mass storage devices  1028  implement the example datastore  380  of  FIG. 3 . 
     The machine executable instructions  1032  of  FIGS. 6-9  may be stored in the mass storage device  1028 , in the volatile memory  1014 , in the non-volatile memory  1016 , and/or on a removable non-transitory computer readable storage medium such as a CD or DVD. 
     A block diagram illustrating an example software distribution platform  1105  to distribute software such as the example computer readable instructions  1032  of  FIG. 10  to third parties is illustrated in  FIG. 11 . The example software distribution platform  1105  may be implemented by any computer server, data facility, cloud service, etc., capable of storing and transmitting software to other computing devices. The third parties may be customers of the entity owning and/or operating the software distribution platform  1105 . For example, the entity that owns and/or operates the software distribution platform  1105  may be a developer, a seller, and/or a licensor of software such as the example computer readable instructions  1032  of  FIG. 10 . The third parties may be consumers (e.g., airline operators), users (e.g., pilots, technicians, etc.), retailers (e.g., aircraft suppliers, aircraft vendors, etc.), OEMs (e.g., aircraft OEMs), etc., who purchase and/or license the software for use and/or re-sale and/or sub-licensing. In the illustrated example, the software distribution platform  1105  includes one or more servers and one or more storage devices. The storage devices store the computer readable instructions  1032 , which may correspond to the example computer readable instructions  600 ,  700 ,  800 ,  900  of  FIGS. 6-9 , as described above. The one or more servers of the example software distribution platform  1105  are in communication with a network  1110 , which may correspond to any one or more of the Internet and/or any of the example networks  360 ,  1026  described above. In some examples, the one or more servers are responsive to requests to transmit the software to a requesting party as part of a commercial transaction. Payment for the delivery, sale and/or license of the software may be handled by the one or more servers of the software distribution platform  1105  and/or via a third party payment entity. The servers enable purchasers and/or licensors to download the computer readable instructions  1032  from the software distribution platform  1105 . For example, the software, which may correspond to the example computer readable instructions  600 ,  700 ,  800 ,  900  of  FIGS. 6-9 , may be downloaded to the example processor platform  1000 , which is to execute the computer readable instructions  1032  to implement one(s) of the example vehicle controllers  102 ,  300 ,  400 ,  500  of  FIGS. 1, 3, 4 , and/or  5 . In some examples, one or more servers of the software distribution platform  1105  periodically offer, transmit, and/or force updates to the software (e.g., the example computer readable instructions  1032  of  FIG. 10 ) to ensure improvements, patches, updates, etc. are distributed and applied to the software at the end user devices (e.g., aircraft control computers, remote electronic units, etc.). 
     From the foregoing, it will be appreciated that the above disclosed methods, apparatus, and articles of manufacture provide observer-based landing control of a vehicle, such as an aircraft. The above disclosed vehicle control apparatus can determine a command to control the vehicle during a flare regime of a flight plan based on determining and/or estimating one or more states of a vehicle parameter during the flare regime. The above disclosed vehicle controllers can perform state feedback margin recovery while increasing robustness at high frequencies. In addition, the above disclosed vehicle controllers may implement adaptive control to control the vehicle when one or more vehicle parameter states are unknown. 
     Example methods, apparatus, systems, and articles of manufacture for observer-based landing control of a vehicle are disclosed herein. Further examples and combinations thereof include the following: 
     Example 1 includes an apparatus comprising at least one memory, and at least one processor to execute instructions to at least in response to determining an aircraft is in a flare regime of a flight plan, determine an estimate state of an aircraft parameter based on an execution of a transfer function of an observer model, the execution of the transfer function based on an altitude command corresponding to the flare regime, determine a gain value based on a measured state of the aircraft parameter, determine an altitude control input based on the estimate state and the gain value, determine an altitude command output based on the altitude control input and longitudinal dynamics of the aircraft, the longitudinal dynamics generated in response to the aircraft executing the altitude command output, and control an elevator of the aircraft based on the altitude command output. 
     Example 2 includes the apparatus of example 1, wherein the altitude command is based on a trajectory from a first position of the aircraft in the flare regime of the flight plan to a second position on a ground surface as a function of time. 
     Example 3 includes the apparatus of example 1 or 2, wherein the aircraft parameter includes at least one of an altitude, a configuration, or an airspeed of the aircraft, and the at least one processor is to map the at least one of the altitude, the configuration, or the airspeed to a look-up table to determine the gain value. 
     Example 4 includes the apparatus of any of examples 1-3, wherein the estimate state is based on one or more measured states including the measured state, the one or more measured states based on at least one of an altitude parameter, an angle of attack parameter, or a sideslip parameter, the at least one of the altitude parameter, the angle of attack parameter, or the sideslip parameter based on a measurement from a sensor, the sensor being an altimeter, an acceleration sensor, a gyro sensor, or an angular rate sensor. 
     Example 5 includes the apparatus of any of examples 1-4, wherein the at least one processor is to determine an observer matrix based on a flight conditions matrix, the flight conditions matrix including values associated with a plurality of flight conditions, and execute the transfer function based on a difference between an identity matrix and the observer matrix to output a state matrix, the state matrix including the estimate state of the aircraft parameter. 
     Example 6 includes the apparatus of any of examples 1-5, wherein the at least one processor is to determine a difference between the altitude command and the altitude command output, and in response to the difference satisfying a threshold, adjust the estimate state of the aircraft parameter based on the difference. 
     Example 7 includes the apparatus of any of examples 1-6, wherein the gain value is a first gain value, and the at least one processor is to determine a second gain value, determine one or more first inputs based on a bounded altitude command and the second gain value, determine a configuration of the aircraft, determine an observer error feedback gain based on a mapping of at least one of the configuration or the aircraft parameter to a look-up table, integrate a difference between the bounded altitude command and the altitude command output, determine one or more second inputs based on at least one of the observer error feedback gain, the aircraft parameter, or the integrated difference, and determine one or more third inputs to the observer model based on a sum of the one or more first inputs and the one or more second inputs. 
     Example 8 includes a non-transitory computer readable storage medium comprising instructions that, when executed, cause at least one processor to at least in response to determining an aircraft is in a flare regime of a flight plan, determine an estimate state of an aircraft parameter based on an execution of a transfer function of an observer model, the execution of the transfer function based on an altitude command corresponding to the flare regime, determine a gain value based on a measured state of the aircraft parameter, determine an altitude control input based on the estimate state and the gain value, determine an altitude command output based on the altitude control input and longitudinal dynamics of the aircraft, the longitudinal dynamics generated in response to the aircraft executing the altitude command output, and control an elevator of the aircraft based on the altitude command output. 
     Example 9 includes the non-transitory computer readable storage medium of example 8, wherein the altitude command is based on a trajectory from a first position of the aircraft in the flare regime of the flight plan to a second position on a ground surface as a function of time. 
     Example 10 includes the non-transitory computer readable storage medium of example 8 or 9, wherein the aircraft parameter includes at least one of an altitude, a configuration, or an airspeed of the aircraft, and the instructions, when executed, cause the at least one processor to map the at least one of the altitude, the configuration, or the airspeed to a look-up table to determine the gain value. 
     Example 11 includes the non-transitory computer readable storage medium of any of examples 8-10, wherein the estimate state is based on one or more measured states including the measured state, the one or more measured states based on at least one of an altitude parameter, an angle of attack parameter, or a sideslip parameter, the at least one of the altitude parameter, the angle of attack parameter, or the sideslip parameter based on a measurement from a sensor, the sensor being an altimeter, an acceleration sensor, a gyro sensor, or an angular rate sensor. 
     Example 12 includes the non-transitory computer readable storage medium of any of examples 8-11, wherein the instructions, when executed, cause the at least one processor to determine an observer matrix based on a flight conditions matrix, the flight conditions matrix including values associated with a plurality of flight conditions, and execute the transfer function based on a difference between an identity matrix and the observer matrix to output a state matrix, the state matrix including the estimate state of the aircraft parameter. 
     Example 13 includes the non-transitory computer readable storage medium of any of examples 8-12, wherein the instructions, when executed, cause the at least one processor to determine a difference between the altitude command and the altitude command output, and in response to the difference satisfying a threshold, adjust the estimate state of the aircraft parameter based on the difference. 
     Example 14 includes the non-transitory computer readable storage medium of any of examples 8-13, wherein the gain value is a first gain value, and the instructions, when executed, cause the at least one processor to determine a second gain value, determine one or more first inputs based on a bounded altitude command and the second gain value, determine a configuration of the aircraft, determine an observer error feedback gain based on a mapping of at least one of the configuration or the aircraft parameter to a look-up table, integrate a difference between the bounded altitude command and the altitude command output, determine one or more second inputs based on at least one of the observer error feedback gain, the aircraft parameter, or the integrated difference, and determine one or more third inputs to the observer model based on a sum of the one or more first inputs and the one or more second inputs. 
     Example 15 includes a method comprising in response to determining an aircraft is in a flare regime of a flight plan, determining an estimate state of an aircraft parameter based on an execution of a transfer function of an observer model, the execution of the transfer function based on an altitude command, determining a gain value based on an aircraft parameter, determining an altitude control input based on the estimate state and the gain value, determining an altitude command output based on the altitude control input and longitudinal dynamics of the aircraft, the longitudinal dynamics generated in response to the aircraft executing the altitude command output, and controlling an elevator of the aircraft based on the altitude command output. 
     Example 16 includes the method of example 15, wherein the aircraft parameter includes at least one of an altitude, a configuration, or an airspeed of the aircraft, and further including mapping the at least one of the altitude, the configuration, or the airspeed to a look-up table to determine the gain value. 
     Example 17 includes the method of example 15 or 16, wherein the estimate state is based on one or more measured states including the measured state, the one or more measured states based on at least one of an altitude parameter, an angle of attack parameter, or a sideslip parameter, the at least one of the altitude parameter, the angle of attack parameter, or the sideslip parameter based on a measurement from a sensor, the sensor being an altimeter, an acceleration sensor, a gyro sensor, or an angular rate sensor. 
     Example 18 includes the method of any of examples 15-17, further including determining an observer matrix based on a flight conditions matrix, the flight conditions matrix including values associated with a plurality of flight conditions, and executing the transfer function based on a difference between an identity matrix and the observer matrix to output a state matrix, the state matrix including the estimate state of the aircraft parameter. 
     Example 19 includes the method of any of examples 15-18, further including determining a difference between the altitude command and the altitude command output, and in response to the difference satisfying a threshold, adjusting the estimate state of the aircraft parameter based on the difference. 
     Example 20 includes the method of any of examples 15-19, wherein the gain value is a first gain value, and further including determining a second gain value, determining one or more first inputs based on a bounded altitude command and the second gain value, determining a configuration of the aircraft, determining an observer error feedback gain based on a mapping of at least one of the configuration or the aircraft parameter to a look-up table, integrating a difference between the bounded altitude command and the altitude command output, determining one or more second inputs based on at least one of the observer error feedback gain, the aircraft parameter, or the integrated difference, and determining one or more third inputs to the observer model based on a sum of the one or more first inputs and the one or more second inputs. 
     Although certain example systems, methods, apparatus, and articles of manufacture have been disclosed herein, the scope of coverage of this patent is not limited thereto. On the contrary, this patent covers all systems, methods, apparatus, and articles of manufacture fairly falling within the scope of the claims of this patent.