the lqg optimal regulation problem for systems with perfect measurements explicit solution properties and application to practical designs the continuous time stationary linear quadratic gaussian lqg optimal regulation problem is considered where the measurements are free of white noise components a simple direct solution in the s domain is derived for the optimal controller for general linear time variant right invertible or left invertible systems the explicit expressions that are found for the controller transference and for the regulator return ratio matrix can be used to obtain a practical suboptimal design in the s domain these expressions are applied to derive simple conditions for the precise recovery of the return ratio matrix of the lqg regulator

the optimal projection equations for reduced order state estimation the singular measurement noise case the optimal projection equations for reduced order state estimation are generalized to allow for singular i e colored measurement noise the noisy and noise free measurements serve as inputs to dynamic and static estimators respectively the optimal solution is characterized by necessary conditions which involve a pair of oblique projections corresponding to reduced estimator order and singular measurement noise intensity

partial cheap control of the time invariant regulator a singular perturbation analysis of the partial cheap control of the linear time invariant regulator is presented in which some but not necessarily all of the control inputs have arbitrarily small cost weighting in the limit the m 2 initial cheap control inputs arc impulsive while the outer solution asymptotically approaches a singular are associated with a dynamical system and matrix riccati equation both of order n m 2 a two time scale decomposition of the regulator problem yields a slow control and a composite control that provide near optimal performance further the partial cheap control results are used to solve the dual almost singular optimal linear filtering problem

on the existence of an optimal observer in singular measurement systems an essential stage in each of the existing methods for singular optimal estimation is to obtain a nonsingular measurement vector which is a linear combination of the original measurement vector and a finite number of its derivatives a necessary and sufficient condition for the existence of such a nonsingular measurement is presented if this condition is satisfied then the existence of an optimal observer is guaranteed the new condition is shown to be considerably simpler and of much wider applicability than a recently published condition which is just a sufficient one the new condition requires just a rank check of a single composite matrix consisting of the system and noise matrices unlike the other condition the existence of an optimal estimator is determined here without carrying out the complex procedures for singular optimal estimation

the singular steady state linear regulator we consider the problem of infimizing the steady state quadratic cost functional whose integrand is given by phi d d phi u ru with r positive semidefinite subject to the constraint dot phi a phi bu with fixed initial state it is shown that there may be two separate cost infima one under the assumption of bounded control energy and one under the additional assumption of partially bounded inputs each of them is a positive semidefinite quadratic function of the initial state whose coefficient matrix is one of the positive semidefinite solutions of a pair of algebraic riccati relations provided there are no system modes which are uncontrollable observable and unstable the cost infimum can be found by solving a sequence of algebraic riccati equations in a reduced state space let b 0 denote the restriction of b to kernel r if the unobservable subspace of the pair d a is the same as the supremal a b 0 invariant subspace contained in kernel d then the coefficient matrix of the

logarithmic control trajectory tracking and formation for nonholonomic vehicles on lie group se 2 abstractthis paper studies the problem of set point stabilisation trajectory tracking and formation tracking for unicycle type vehicles by taking advantage of the exponential coordinates and the other mathematical tools provided by the lie group setting of the special euclidean group se 2 motivated by recent developments in geometric control approaches for holonomic systems we first study the stabilisation problem for nonholonomic constrained kinematic systems by improving the logarithmic stabilising control laws in such a way that they can satisfy nonholonomic constraints too we then extend the control design to the problem of trajectory tracking by proposing auxiliary systems and investigating the conditions for which the adjoint map in the lie algebra preserves the velocity constraint this leads to a global control law which is valid for general time varying as well as non smooth trajectories the tracking control law is also applied to the problem of leader follower formation tracking by constr

controlled lagrangians and the stabilization of mechanical systems ii potential shaping for pt i see ibid vol 45 p 2253 70 2000 we extend the method of controlled lagrangians cl to include potential shaping which achieves complete state space asymptotic stabilization of mechanical systems the cl method deals with mechanical systems with symmetry and provides symmetry preserving kinetic shaping and feedback controlled dissipation for state space stabilization in all but the symmetry variables potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables the approach also extends the method of controlled lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline

a generalized inverse solution to the discrete time singular riccati equation a closed form solution to the discrete time singular riccati equation is presented which is based on the moore penrose matrix inverse applications to deadbeat control and stabilizability are discussed

a geometric approach for quadrotor trajectory tracking control this paper investigates the trajectory tracking problem for quadrotor with attitude finite time convergence via geometric approach first a global geometric dynamic description is presented on the special euclidean group se 3 and the trajectory tracking control is decomposed into two cascaded tracking control loops the position tracking control loop and the attitude tracking control loop then based on the fact that the attitude tracking loop is a fast loop a finite time controller based on the exponential coordinate is proposed to speed up the response rate of the attitude control loop so that the artificial singularity and redundancy can be avoided in addition a backstepping controller is designed for the position tracking loop to construct the thrust magnitude control input for the position dynamics and the reference rotation matrix for the attitude tracking loop finally the numerical simulation results are presented to demonstrate the effectiveness of this trajectory tracking strategy

minimal order wiener filter for a system with exact measurements necessary and sufficient conditions for the existence of an optimal steady state state estimator are derived under the assumption that this estimator is a linear functional of the measurements and a finite number of derivatives of the exact measurements our conditions are shown to be dual to the generalized legendre clebsch conditions of the dual optimal singular regulator a separation principle is derived and it is shown that as all process and measurement noise vanishes the error covariance of our filter converges to a null matrix

optimal partitioning for classification and regression trees an iterative algorithm that finds a locally optimal partition for an arbitrary loss function in time linear in n for each iteration is presented the algorithm is a k means like clustering algorithm that uses as its distance measure a generalization of kullback s information divergence moreover it is proven that the globally optimal partition must satisfy a nearest neighbour condition using divergence as the distance measure these results generalize similar results of l breiman et al 1984 to an arbitrary number of classes or regression variables and to an arbitrary number of bills experimental results on a text to speech example are provided and additional applications of the algorithm including the design of variable combinations surrogate splits composite nodes and decision graphs are suggested

intrinsic observer based stabilization for simple mechanical systems on lie groups this paper presents a dynamic observer for a class of simple mechanical systems on lie groups this observer provides velocity estimates based on configuration measurements the observer is textit intrinsic so its performance does not depend on the choice of coordinates and it is textit coordinate free in the sense that the equations may be written explicitly without specifying coordinates for the configuration space our main result is obtained by specializing a previous result of aghannan and rouchon concerning velocity estimation of simple mechanical systems on riemannian manifolds to such systems on lie groups this specialization is nonobvious and extremely powerful further we extend the original result to include velocity dependent external forces this estimator combined with a coordinate free formulation of passivity based state feedback control allows the construction of a coordinate free intrinsic dynamic output feedback compensator this is to our knowledge the first time such a result has been reported explicit expressions are computed for the lie groups so 3 and se 3 allowing easy specialization to practical problems of rigid body motion the theory is illustrated via application to the axisymmetric top and to a six degrees of freedom microelectromechanical system

pose estimation using line based dynamic vision and inertial sensors an observer problem from a computer vision application is studied rigid body pose estimation using inertial sensors and a monocular camera is considered and it is shown how rotation estimation can be decoupled from position estimation orientation estimation is formulated as an observer problem with implicit output where the states evolve on so 3 a careful observability study reveals interesting group theoretic structures tied to the underlying system structure a locally convergent observer where the states evolve on so 3 is proposed and numerical estimates of the domain of attraction is given further it is shown that given convergent orientation estimates position estimation can be formulated as a linear implicit output problem from an applications perspective it is outlined how delayed low bandwidth visual observations and high bandwidth rate gyro measurements can provide high bandwidth estimates this is consistent with real time constraints due to the complementary characteristics of the sensors which are fused in a multirate way

configuration flatness of lagrangian systems underactuated by one control lagrangian control systems that are differentially flat with flat outputs that depend only on configuration variables are said to be configuration flat we provide a complete characterization of configuration flatness for systems with n degrees of freedom and n 1 controls whose range of control forces only depends on configuration and whose lagrangian has the form of kinetic energy minus potential the method presented allows us to determine if such a system is configuration flat and if so provides a constructive method for finding all possible configuration flat outputs our characterization relates configuration flatness to riemannian geometry we illustrate the method with two examples

decision tree design from a communication theory standpoint a communication theory approach to decision tree design based on a top town mutual information algorithm is presented it is shown that this algorithm is equivalent to a form of shannon fano prefix coding and several fundamental bounds relating decision tree parameters are derived the bounds are used in conjunction with a rate distortion interpretation of tree design to explain several phenomena previously observed in practical decision tree design a termination rule for the algorithm called the delta entropy rule is proposed that improves its robustness in the presence of noise simulation results are presented showing that the tree classifiers derived by the algorithm compare favourably to the single nearest neighbour classifier

invariant feedback control for the kinematic car on the sphere abstract the design of an invariant tracking control law for the kinematic car driving on a sphere is discussed using a lie group framework a left invariant description on so 3 is derived basic geometric considerations allow a direct comparison of the model with the planar case using a geometrically motivated invariant tracking error on s 2 an invariant feedback design is proposed finally one possible design of an invariant asymptotic observer is sketched

an experimental evaluation of simplicity in rule learning while recent research on rule learning has focused largely on finding highly accurate hypotheses we evaluate the degree to which these hypotheses are also simple that is small to realize this we compare well known rule learners such as cn2 ripper part foil and c5 0 rules with the benchmark system sl 2 that explicitly aims at computing small rule sets with few literals the results show that it is possible to obtain a similar level of accuracy as state of the art rule learners using much smaller rule sets

tracking for fully actuated mechanical systems a geometric framework we present a general framework for the control of lagrangian systems with as many inputs as degrees of freedom relying on the geometry of mechanical systems on manifolds we propose a design algorithm for the tracking problem the notions of error function and transport map lead to a proper definition of configuration and velocity error these are the crucial ingredients in designing a proportional derivative feedback and feedforward controller the proposed approach includes as special cases a variety of results on control of manipulators pointing devices and autonomous vehicles our design provides particular insight into both aerospace and underwater applications where the configuration manifold is a lie group

stabilization of relative equilibria for underactuated systems on riemannian manifolds steady motions of mechanical systems with symmetry are stabilized via a potential shaping and damping control a general methodology based on riemannian geometry tools provides exponential stabilization over the full phase space

a riccati equation approach to the singular lqg problem abstract the problem of optimal fixed order dynamic compensation for the singular lqg problem is considered necessary conditions characterizing the optimal compensator for the case involving both singular measurement noise and singular control weighting are given the solution consists of a set of two algebraic riccati equations and two lyapunov equations coupled by three projection matrices one projection is the standard order reduction projection while the other two projections reflect the two types of singularity that exist in the system the three projections are shown to satisfy disjointness conditions in addition to order reduction an advantage of the fixed structure approach is that differentiation which is often undersirable from a practical point of view and which may exist in the unconstrained optimal control can be avoided it is shown that the fixed order compensator agrees with the unconstrained solution when the latter possesses the same number of differentiations as are included in the prespecified controller structure and when the order is selected appropriately

criteria for selecting a variable in the construction of efficient decision trees two variable selection criteria are proposed for converting a decision table to a near optimum decision tree in the sense of minimal average cost of testing a criterion q is introduced that is based on the potential of a decision table the previously known criterion loss and q are combined into a third criterion o the performance of the three criteria is examined both theoretically and experimentally of most importance is that q and o do not select a nonessential variable while loss may do so it is also shown that the performance of the three criteria is not worse than that of any other known heuristics at least for a particular example the algorithm requires at most o l sup 2 2 sup l operations where l is the arity of an input table

an intrinsic observer for a class of lagrangian systems we propose a new design method of asymptotic observers for a class of nonlinear mechanical systems lagrangian systems with configuration position measurements our main contribution is to introduce a state position and velocity observer that is invariant under any changes of the configuration coordinates the observer dynamics equations as the euler lagrange equations are intrinsic the design method uses the riemannian structure defined by the kinetic energy on the configuration manifold the local convergence is proved by showing that the jacobian of the observer dynamics is negative definite contraction for a particular metric defined on the state space a metric derived from the kinetic energy and the observer gains from a practical point of view such intrinsic observers can be approximated when the estimated configuration is close to the true one by an explicit set of differential equations involving the riemannian curvature tensor these equations can be automatically generated via symbolic differentiations of the metric and potential up to order two numerical simulations for the ball and beam system an example where the scalar curvature is always negative show the effectiveness of such approximation when the measured positions are noisy or include high frequency neglected dynamics

asymptotic stabilization of the inverted equilibrium manifold of the 3 d pendulum using non smooth feedback the 3 d pendulum consists of a rigid body supported at a fixed pivot with three rotational degrees of freedom it is acted on by gravity and it is fully actuated by control forces in almost global stabilization of the inverted equilibrium manifold was studied using a smooth globally defined feedback here we study the problem of almost global stabilization of the inverted equilibrium manifold using non smooth feedback of angular velocity and a reduced attitude vector of the 3 d pendulum the importance of the non smooth feedback is that the almost global domain of attraction is a geometrically simple set that excludes the hanging attitude manifold unlike the closed loop for a 3 d pendulum with a smooth controller the closed loop designed in this paper does not exhibit a performance constraint these new results are based on lyapunov analysis of the non smooth closed loop 3 d pendulum

a statistical heuristic feature selection criterion for decision tree induction the authors present a statistical heuristic feature selection criterion for constructing multibranching decision trees in noisy real world domains real world problems often have multivalued features to these problems multibranching decision trees provide a more efficient and more comprehensible solution that binary decision trees the authors propose a statistical heuristic criterion the symmetrical tau and then discuss its consistency with a bayesian classifier and its built in statistical test the combination of a measure of proportional reduction in error and cost of complexity heuristic enables the symmetrical tau to be a powerful criterion with many merits including robustness to noise fairness to multivalued features and ability to handle a boolean combination of logical features and middle cut preference the tau criterion also provides a natural basis for prepruning and dynamic error estimation illustrative examples are also presented

the properties of reduced order minimum variance filters for systems with partially perfect measurements the problem of the finite time reduced order minimum variance full state estimation of linear continuous time invariant systems is considered in cases where the output measurement is partially free of corrupting white noise components the structure of the optimal filter is obtained and a link between this structure and the structure of the system invariant zeros is established using expressions that are derived in closed form for the invariant zeros of the system simple sufficient conditions are obtained for the existence of the optimal filter in the stationary case the structure and the transmission properties of the stationary filter for general left invertible systems are investigated a direct relation between the optimal filter and a particular minimum order left inverse of the system is obtained a simple explicit expression for the filter transfer function matrix is also derived the expression provides an insight into the mechanism of the optimal estimation

abstractions of hamiltonian control systems given a control system and a desired property an abstracted system is a reduced system that preserves the property of interest while ignoring modeling detail in previous work abstractions of linear and nonlinear control systems were considered while preserving reachability properties in this paper we consider the abstraction problem for hamiltonian control systems where in addition to the property of interest we also preserve the hamiltonian structure of the control system we show how the hamiltonian structure of control systems can be exploited to simplify the abstraction process we then focus on local accessibility preserving abstractions and provide conditions under which local accessibility properties of the abstracted hamiltonian system are equivalent to the local accessibility properties of the original hamiltonian control system

configuration controllability of simple mechanical control systems in this paper we present a definition of configuration controllability for mechanical systems whose lagrangian is kinetic energy with respect to a riemannian metric minus potential energy a computable test for this new version of controllability is derived this condition involves an object that we call the symmetric product of particular interest is a definition of equilibrium controllability for which we are able to derive computable sufficient conditions examples illustrate the theory

coordinate independent adaptive attitude tracking control design for spacecraft robust to time varying system uncertainties abstractin this paper we consider the adaptive attitude control of spacecraft with time varying inertial properties we use a coordinate independent approach for the purpose of designing the control and estimation laws in terms of the rotation matrices representing the spacecraft body frame and reference tracking signals this method helps to overcome the difficulties regarding the attitude representation on so 3 such as ambiguities associated with quaternion representation and inherent singularities inside euler parameters we model the time variations in inertial parameters in two different ways and design adaptive control schemes for each case as the first uncertain dynamic model we consider a setting of spacecraft with multiple moving appendages and based on this model design an adaptive control scheme with three different versions where frobenious norm is used in measuring the deviation of the estimated inertia tensors from their actual values the proposed adaptive control scheme is later ex

a geometric approach to the singular filtering problem we consider the least squares filtering problem for a stationary gaussian process when the observation is not fully corrupted by white noise the so called singular case an optimal estimator is constructed consisting of an integrating part which is as in the regular case computed from a spectral factorization or an equivalent matrix problem and a differentiating part whose parameters are computed from a single matrix equation this improves on older results which either work under restrictive assumptions or describe the solution only as the result of some nested algorithm

rotational motion control of a spacecraft this note describes a systematic procedure for the control synthesis of a rigid spacecraft using the energy shaping method the geometric concept of a mechanical system in a coordinate independent form is used to derive a control algorithm for the euler poincare equations the main result of this note is a specialization of the method on the unit quaternion group this note is concluded with the examples of the potential functions and implementation for the three axis attitude control problem

designing storage efficient decision trees the problem of designing storage efficient decision trees from decision tables is examined it is shown that for most cases the construction of the storage optimal decision tree is an np complete problem and therefore a heuristic approach to the problem is necessary a systematic procedure analogous to the information theoretic heuristic is developed the algorithm has low computational complexity and performs well experimentally

composite adaptive control of robot manipulators abstract adaptive control of linear time invariant single input single output systems has been extensively studied and a number of globally convergent controllers have been derived while extensions of the results to non linear or multivariable systems have rarely been achieved similar global convergence properties can indeed be obtained in the case of robot manipulators an important and unique class of non linear multi input multi output dynamic systems based on the observation that the parameter uncertainty is reflected in both the tracking error in joint motion and the prediction error in the joint torques or the power input we recently proposed a new class of adaptive robot controllers the parameter adaptation of which is driven by both tracking error and prediction error in this paper following a brief review of our earlier globally convergent direct adaptive controller we provide a detailed analysis of these composite adaptive controllers results on global asymptotic and exponential tracking convergence are established and confirmed by simulation

passivity based adaptive attitude control of a rigid spacecraft an adaptive control scheme for the attitude control of a rigid spacecraft is derived using a linear parameterization of the equation of motion the tracking error is described with the euler parameter vector global convergence of the tracking error to zero is shown using passivity theory this allows for the use of time varying positive definite feedback gain matrices and the results can easily be extended to other passive parameter update laws

passive decomposition of mechanical systems with coordination requirement we show the fundamental passive decomposition property of general mechanical systems on a n dim configuration manifold m i e when endowed with a submersion h m n where n is a m dim manifold m n their lagrangian dynamics with the kinetic energy as the lagrangian can always be decomposed into 1 shape system describing the m dim dynamics of h q on n 2 locked system representing the n m dim dynamics along the level set of h and 3 energetically conservative coupling between them the locked and shape systems also individually inherit the lagrangian structure and passivity of the original dynamics we exhibit and analyze geometric and energetic properties of the passive decomposition in a coordinate free manner an illustrative example on so 3 is also provided

the geometric convexity on se 3 and its application to the formation tracking in multi vehicle systems abstractthis paper considers the problem of geometric convexity on special euclidean group se 3 and its application to the formation tracking in multi vehicle systems motivated by the convex hull on euclidean space the specific expression of geodesic connecting two points on se 3 is obtained based on the pontryagin s minimum principle then it is extended to the geometric convex combination for multiple points based on which the virtual systems on se 3 is given to be used in the application of formation tracking problem in light of the geometric convex combination and virtual systems on se 3 a consensus based tracking protocol is proposed to guarantee that the formation is achieved under the directed acyclic graphs finally two numerical examples are provided to demonstrate the validity of the theoretical results

an intrinsic pid controller for mechanical systems on lie groups this paper shows how integral action may be implemented intrinsically in the general setting of fully actuated mechanical systems on lie groups when combined with an intrinsic formulation of pd control integral action ensures that a suitably defined configuration tracking error will converge to zero in response to constant velocity commands and disturbance forces convergence is locally exponential and almost global and is robust to bounded parametric uncertainty for more general bounded commands and disturbances the tracking error can be made arbitrarily small by choosing sufficiently large controller gains a separation principle allows the addition of an intrinsic velocity observer to complete a geometric analog to the familiar output feedback pid controller for second order linear systems the controller extends naturally to accommodate tracking of equivariant output functions the result is explicitly shown for the lie group so 3 and supported by simulations of a 6dof quadrotor model

application of information theory to the construction of efficient decision trees the problem of conversion of decision tables to decision trees is treated in most cases the construction of optimal decision trees is an np complete problem and therefore a heuristic approach to this problem is necessary in this heuristic approach an application of information theoretic concepts to construct efficient decision trees for decision tables which may include don t care entries is made in contrast to most of the existing heuristic algorithms this algorithm is systematic and is intuitively appealing from an information theoretic standpoint the algorithm has low design complexity and yet provides near optimal decision trees

state estimation for linear systems with observations partially corrupted by noise abstract this paper exploits the fact that any row vector of the observability matrix applied for transforming the state converts the latter to the new state component in the form of some derivative of the output component using the same but appropriately chosen vectors for transforming the system with the observation not fully corrupted by white noise we can accurately determine some state components these vectors create the basis for the l dimensional subspace of transformation vectors to the new accurately determinable state components using this basis the state transformation is constructed which in one step converts the singular linear filtering problem to a nonsingular one with state dimension decreased by l

the optimal projection equations for static and dynamic output feedback the singular case oblique projections have been shown to arise naturally in both static and dynamic optimal design problems for static controllers an oblique projection was inherent in the early work of levine and athans while for dynamic controllers an oblique projection was developed by hyland and bernstein this note is motivated by the following natural question what is the relationship between the oblique projection arising in optimal static output feedback and the oblique projection arising in optimal fixed order dynamic compensation we show that in nonstrictly proper optimal output feedback there are indeed three distinct oblique projections corresponding to singular measurement noise singular control weighting and reduced compensator order moreover we unify the levine athans and hyland bernstein approaches by rederiving the optimal projection equations for combined static dynamic nonstrictly proper output feedback in a form which clearly illustrates the role of the three projections in characterizing the optimal feedback gains even when the dynamic component of the nonstrictly proper controller is of full order the controller is characterized by four matrix equations which generalize the standard lqg result

extended limiting forms of optimum observers and lqg regulators the general problem of optimal estimation in singular observation systems is considered by generalizing the limiting procedure of friedland explicit and closed expressions for the transfer matrices of the optimum observer as well as for the optimal control law in the singular measurement lqg problem are derived the number of integrators that are required for the implementation of the singular optimum observer is shown for square systems to be equal to the number of the system s zeros the closed form of the optimum observer given here is advantageous as compared with existing procedures structural properties of the singular observation problem are discussed and the role of the zeros of the system in such problems is clarified the dual results for the case of stochastic cheap control are also given

stabilization of a 3d axially symmetric pendulum stabilizing controllers are developed for a 3d pendulum assuming that the pendulum has a single axis of symmetry and that the center of mass lies on the axis of symmetry this assumption allows development of a reduced model that forms the basis for controller design and global closed loop analysis this reduced model is parameterized by the constant angular velocity component of the 3d pendulum about its axis of symmetry several different controllers are proposed controllers based on angular velocity feedback only asymptotically stabilize the hanging equilibrium then controllers are introduced based on angular velocity and reduced attitude feedback that asymptotically stabilize either the hanging equilibrium or the inverted equilibrium these problems can be viewed as stabilization of a lagrange top finally if the angular velocity about the axis of symmetry is assumed to be zero controllers are introduced based on angular velocity and reduced attitude feedback that asymptotically stabilize either the hanging equilibrium or the inverted equilibrium this problem can be viewed as stabilization of a spherical pendulum

brief paper reduced order state estimation for linear systems with exact measurements necessary and sufficient conditions are derived for the existence of reduced order steady state optimal linear state estimators for continuous linear dynamical systems when some output measurements are noise free these conditions are shown to be dual to the generalized strengthened legendre clebsch conditions for the extremal controls of a dual singular regulator when the order of singularity is at most two the optimal estimators are designed without the use of luenberger observers

singular optimal control a geometric approach linear quadratic singular optimal control problem is solved for nonminimum phase and noninvertible systems a state space decomposition is obtained and a reduced order nonsingular subproblem is solved the optimal stabilizing input of the singular problem has been found when there are no transmission zeros on the imaginary axis

direct solution to the general reduced order stochastic observation problem the stochastic optimal state observation problem is considered for a general linear continuous time invariant system with unmeasurable stationary inputs and measurement outputs that may be at least in part perfect a general solution to the problem is obtained by processing the perfect measurements through a specific differentiation transformation scheme in order to extract the maximum accurate information on the system states using this information the original system is transformed to a new reduced order model whose measurements are corrupted by a white noise of non singular intensity matrix a minimum order full state estimator to the original system is then constructed by combining the outputs of any full order observer to the reduced order model and the perfect combinations of the system states that were derived by the differentiation transformation scheme a solution to the general singular kalman filtering problem is then obtained by minimizing the variance of the estimation error of the obser

asymptotic smooth stabilization of the inverted 3 d pendulum the 3 d pendulum consists of a rigid body supported at a fixed pivot with three rotational degrees of freedom it is acted on by gravity and it is fully actuated by control forces the 3 d pendulum has two disjoint equilibrium manifolds namely a hanging equilibrium manifold and an inverted equilibrium manifold the contribution of this paper is that two fundamental stabilization problems for the inverted 3 d pendulum are posed and solved the first problem asymptotic stabilization of a specified equilibrium in the inverted equilibrium manifold is solved using smooth and globally defined feedback of angular velocity and attitude of the 3 d pendulum the second problem asymptotic stabilization of the inverted equilibrium manifold is solved using smooth and globally defined feedback of angular velocity and a reduced attitude vector of the 3 d pendulum these control problems for the 3 d pendulum exemplify attitude stabilization problems on the configuration manifold so 3 in the presence of potential forces lyapunov analysis and nonlinear geometric methods are used to assess global closed loop properties yielding a characterization of the almost global domain of attraction for each case

nonholonomic control systems on riemannian manifolds this paper gives a general formulation of the theory of nonholonomic control systems on a riemannian manifold modeled by second order differential equations and using the unique riemannian connection defined by the metric the main concern is to introduce a reduction scheme replacing some of the second order equations by first order equations the authors show how constants of motion together with the nonholonomic constraints may be combined to yield such a reduction the theory is applied to a particular class of nonholonomic control systems that may be thought of as modeling a generalized rolling ball this class reduces to the classical example of a ball rolling without slipping on a horizontal plane

a simple solution to the singular linear minimum variance estimation problem a simple expression is obtained for the transfer function matrix of the minimum variance estimator for the states of a linear stationary continuous time right invertible system whose output is measured perfectly using the s domain approach it is shown that the optimal estimator first finds the driving noise input that achieves when applied on the minimum phase image model of the system an output spectrum which is identical to the measurement spectrum this input is then applied on a state space representation of the minimum phase image to produce the optimal estimate

on the topological structure of attraction basins for differential inclusions abstract we show that when a compact set is globally asymptotically stable under the action of a differential inclusion satisfying certain regularity properties there exists a smooth differential equation rendering the same compact set globally asymptotically stable the regularity properties assumed in this work stem from the consideration of krasovskii filippov solutions to discontinuous differential equations and the robustness of asymptotic stability under perturbation in particular the results in this work show that when a compact set cannot be globally asymptotically stabilized by continuous feedback due to topological obstructions it cannot be robustly globally asymptotically stabilized by discontinuous feedback either the results follow from converse lyapunov theory and parallel what is known for the local stabilization problem

brief paper the spring paradigm in tracking control of simple mechanical systems an intrinsic formulation of geometric proportional derivative tracking control for fully actuated mechanical systems is developed the region of stability is determined directly from the size of the system s injectivity radius and for a restricted set of control problems the system s locus of cut points about a desired reference point exponential stability is obtained under certain boundedness conditions for controlled motion along a geodesic the proffered scheme yields a particularly simple and elegant manifestation of the underlying use of the mass spring damper paradigm in the control design methodology

the optimal reduced order estimator for systems with singular measurement noise the optimal reduced order estimator is completely characterized by necessary conditions resulting from the optimal projection equations the solution consists of one riccati equation and two lyapunov equations coupled by two projections explicit expressions for all of the estimator parameters are given the relation between the reduced order singular estimator and the full order optimal singular estimator which is of reduced order itself is investigated it is shown that under certain conditions the optimal estimator is recovered from the reduced order estimator

new class of control laws for robotic manipulators part 1 non adaptive case a new class of exponentially stabilizing control laws for joint level control of robot arms is introduced it has recently been recognized that the non linear dynamics associated with robotic manip

global stabilization of spherical orientation by synergistic hybrid feedback with application to reduced attitude tracking for rigid bodies in this paper we propose a hybrid feedback based on a synergistic potential function that achieves global asymptotic stabilization of a desired orientation on the n sphere with a nominal robustness to measurement disturbances a task that is not possible by classical feedback be it smooth nonsmooth periodic or any combination thereof due to the topological structure of the sphere we extend this basic result to a tracking controller for the reduced attitude or pointing direction of a rigid body and provide a method to remove jumps in the controlled torque by backstepping the proposed hybrid feedback is compared with a similar smooth feedback in simulation where it is illustrated that the hybrid feedback overcomes performance limitations inherent to the smooth feedback we provide two examples of a synergistic potential function one defined on a general sphere and the other on the unit circle

the optimal projection equations for fixed order dynamic compensation first order necessary conditions for quadratically optimal steady state fixed order dynamic compensation of a linear time invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form in contrast to the pair of matrix riccati equations for the full order lqg case the optimal steady state fixed order dynamic compensator is characterized by four matrix equations two modified riccati equations and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the compensator and which determines the optimal compensator gains the coupling represents a graphic portrayal of the demise of the classical separation principle for the reduced order controller case

on the optimal unbiased functional filtering presents a simple solution to the optimal unbiased reduced order or functional filtering problem for linear time varying systems necessary and sufficient conditions for the existence of the obtained filter are given stability and convergence conditions are developed for the time invariant systems both continuous and discrete time cases are considered

the attitude control problem a general framework for the analysis of the attitude tracking control problem for a rigid body is presented a large family of globally stable control laws is obtained by using the globally nonsingular unit quaternion representation in a lyapunov function candidate whose form is motivated by the consideration of the total energy of the rigid body the controllers share the common structure of a proportional derivative feedback plus some feedforward which can be zero the model independent case the coriolis torque compensation or an adaptive compensation these controller structures are compared in terms of the requirement on the a priori model information guaranteed transient performance and robustness the global stability of the luh walker paul robot end effector controller is also analyzed in this framework

limiting forms of optimal observers halevi and palmor 1986 presented closed form expressions for optimal observers for singular measurement systems two assumptions were made there i the measurement is totally singular and ii the number of outputs is less than or equal to the number of stochastic inputs these two assumptions are relaxed in this paper and the optimal observer for the most general singular measurement case is given

a general riccati equation solution to the deadbeat control problem it is well known that the state of a controllable system can be driven to zero in minimum time for arbitrary initial condition by the time varying kalman gain sequence computed via a singular riccati equation this paper shows how a constant deadbeat control feedback which will accomplish the same result in the same minimum time can always be found via the same riccati equation

configuration controllability of simple mechanical control systems in this paper we present a definition of configuration controllability for mechanical systems whose lagrangian is kinetic energy with respect to a riemannian metric minus potential energy a computable test for this new version of controllability is derived this condition involves an object which we call the symmetric product of particular interest is a definition of equilibrium controllability for which we are able to derive computable sufficient conditions examples illustrate the theory