a new approach to the perfect regulation and the bounded peaking in linear multivariable control systems this paper presents a new approach to the perfect regulation p r and the bounded peaking b p in linear multivariable control systems based on the pole and the eigenvector assignment technique roughly speaking the p r represents an ideal control action which reduces the settling time to 0 while the b p simply means the bounded overshoot in this ideal situation simple frequency domain characterizations of the p r and the b p are derived they reveal some invariance properties of the p r and the b p that provide a powerful tool for achieving the p r and the b p the existence condition for the p r is derived which turns out to be identical to the result obtained in the optimal regulator theory this result is extended to a more general control objective of attaining the p r for one output while keeping the b p for another output a condition on which the p r is realized by an output feedback is also derived a simple design algorithm is proposed for achieving the p r which is essentially the eigenvector assignment procedure finally an application to a real system is discussed

on optimal pole assignment in a specified region in this paper the problem of pole assignment and linear quadratic design have been amalgamated a design method that has the merits of both approaches is presented and the problem of assigning the poles in a specified region is solved the characterizations for quadratic cost functions have been studied and these results used to assign poles in real schur form in a region so that the optimality is maintained designed procedures have been elaborated with examples

brief constrained linear state estimation a moving horizon approach this article considers moving horizon strategies for constrained linear state estimation additional information for estimating state variables from output measurements is often available in the form of inequality constraints on states noise and other variables formulating a linear state estimation problem with inequality constraints however prevents recursive solutions such as kalman filtering and consequently the estimation problem grows with time as more measurements become available to bound the problem size we explore moving horizon strategies for constrained linear state estimation in this work we discuss some practical and theoretical properties of moving horizon estimation we derive sufficient conditions for the stability of moving horizon state estimation with linear models subject to constraints on the estimate we also discuss smoothing strategies for moving horizon estimation our framework is solely deterministic

correspondence author s reply to comments on performance evaluation of ukf based nonlinear filtering it is stated in the above mentioned comment that the main result of the paper xiong zhang et al 2006 performance evaluation of ukf based nonlinear filtering automatica 42 2 261 270 can be extended to a class of filters such as the extended kalman filter ekf as we show here this belief can be justified in a rigorous way even for the nonlinear stochastic system with a nonlinear measurement equation

a successive optimal construction procedure for state feedback gains abstract this paper studies a successive optimal construction procedure of state feedback gains this topic was first studied in the context of the pole assignment problem for lq linear quadratic regulators but the selection of weighting matrices in each successive step was restricted in previous researches in this paper we consider more general selections of weighting matrices and give extended results in both the continuous time and the discrete time cases

brief paper state estimation for linear systems with state equality constraints this paper deals with the state estimation problem for linear systems with linear state equality constraints using noisy measurements which are available from the observable system we construct the optimal estimate which also satisfies linear equality constraints for this purpose after reviewing modeling problems in linear stochastic systems with state equality constraints we formulate a projected system representation by using the constrained kalman filter for the projected system and comparing its filter riccati equation with those of the unconstrained and the projected kalman filters we clearly show without using optimality that the constrained estimator outperforms the other filters for estimating the constrained system state finally a numerical example is presented which demonstrates performance differences among those filters

target tracking problems subject to kinematic constraints filtering problems with kinematic constraints which may arise in target tracking problems are considered a novel approach which treats kinematic constraints as additional fictitious or pseudomeasurements is proposed a numerical example is provided to show the technical feasibility of the proposed idea for target tracking problems this example shows that the proposed method can improve estimation accuracy significantly for velocity and acceleration states in the tracking problem however it is noted that the tracking performance may be deteriorated if the constraints do not properly represent the target characteristics and a small r sub c is chosen

a smoothly constrained kalman filter this paper presents the smoothly constrained kalman filter sckf for nonlinear constraints a constraint is any relation that exists between the state variables constraints can be treated as perfect observations but linearization errors can prevent the estimate from converging to the true value therefore the sckf iteratively applies nonlinear constraints as nearly perfect observations or equivalently weakened constraints integration of new measurements is interlaced with these iterations which reduces linearization errors and hence improves convergence compared to other iterative methods the weakening is achieved by artificially increasing the variance of the nonlinear constraint the paper explains how to choose the weakening values and when to start and stop the iterative application of the constraint

a revisit to inverse optimality of linear systems in this article we revisit the problem of inverse optimality for linear systems by applying certain explicit formulae for coprime matrix fraction descriptions cmfd of linear systems we propose a necessary and sufficient condition for a given stable state feedback law to be optimal for some quadratic performance index compared to existing results in the literature the proposed condition is simpler to check and interpret moreover it reduces the redundancy in the solutions of the associated algebraic riccati equation are as a direct application of the proposed results we consider the problem of inverse optimality of observer based state feedback to be specific for the case where the state is not fully known we consider the inverse optimality problem of an observer based state feedback for the closed loop system augmented by an observer more precisely it is shown that the observer based state feedback is inverse optimal for the closed loop system with some general forms of cost functions on

linear quadratic optimal output feedback control for systems with poles in a specified region the problem of output feedback linear quadratic regulator synthesis with regional pole constraints is studied the synthesis algorithm is presented and its convergence is also proved the effectiveness of the algorithm is illustrated by an example

generalized robustness of optimally of linear quadratic regulators robustness of the optimality of linear quadratic lq optimal regulators is studied it is shown that under a mild assumption optimality of lq regulators is preserved under small perturbations on both f and g matrices this is made possible by allowing modifications on both weighting parameters q and r and it also extends the existing results where perturbations on f only are allowed it is also observed that this modification leads to a possible change in gain margin a numerical example is discussed in detail to illustrate the results

cross standard form a solution to improve a given controller with h 2 or h specifications this paper introduces in cross standard form csf as a solution to the inverse optimal control problem that is the csf is a canonical standard problem whose unique h or h 2 optimal controller is a given controller from the control design point of view the general idea is to apply the csf to a given controller in order to set up a standard problem which can be completed to handle frequency domain h 2 or h specification the analytical formulation of the csf proposed in this paper can be applied to reduced full or augmented order compensators or two degree of freedom compensations numerical and academic examples are given

receding horizon nonlinear kalman rnk filter for state estimation this technical note presents a new receding horizon nonlinear kalman rnk filter for state estimation in nonlinear systems with state constraints such problems appear in almost all engineering disciplines unlike the moving horizon estimation mhe approach the rnk filter formulation follows the kalman filter kf predictor corrector framework the corrector step is solved as an optimization problem that handles constraints effectively the performance improvement and robustness of the proposed estimator vis a vis the extended kalman filter ekf are demonstrated through nonlinear examples these examples also demonstrate the computational advantages of the proposed approach over the mhe formulation the computational gain is due to the fact that the proposed rnk formulation avoids the repeated integration within an optimization loop that is required in an mhe formulation further the proposed formulation results in a quadratic program qp problem for the corrector step when the measurement model is linear irrespective of the state propagation model in contrast a nonlinear programming problem nlp needs to be solved when an mhe formulation is used for such problems also the proposed filter for unconstrained linear systems results in a kf estimate for the current instant and smoothed estimates for the other instants of the receding horizon

state estimation for linear and non linear equality constrained systems this article addresses the state estimation problem for linear and non linear systems for the case in which prior knowledge is available in the form of an equality constraint the equality constrained kalman filter kf is derived as the maximum a posteriori solution to the equality constrained state estimation problem for linear and gaussian systems and is compared to alternative algorithms then four novel algorithms for non linear equality constrained state estimation based on the unscented kf are presented namely the equality constrained unscented kf the projected unscented kf the measurement augmentation unscented kf and the constrained unscented kf finally these methods are compared on linear and non linear examples

linear quadratic control with stability degree constraint abstract the problem of static state feedback linear quadratic lq optimal control subject to a prescribed degree of stability for the closed loop system is considered in this paper a necessary optimality condition is given via the lagrange multiplier method a globally convergent algorithm is provided to solve the optimization problem it is shown that the algorithm recovers the standard lq feedback gain provided the desired stability degree is small enough to be within the range by the standard lq design as for other cases the optimum occurs on the boundary of the region a numerical example shows that the proposed algorithm provides a better design compared to the existing methods

use of a kinematic constraint in tracking constant speed maneuvering targets the use of a kinematic constraint as a pseudomeasurement in the tracking of constant speed maneuvering targets is considered the kinematic constraint provides additional information about the target motion that can be processed as a pseudomeasurement to improve tracking performances a new formulation of the constraint equation is presented and the rationale for the new formulation is discussed the filter using the kinematic constraint as a pseudomeasurement is shown to be unbiased and sufficient conditions for stochastic stability of the filter are given simulated tracking results are given to demonstrate the potential that the new formulation provides for improving tracking performance

model predictive control tuning by controller matching the effectiveness of model predictive control mpc in dealing with input and state constraints during transient operations is well known however in contrast with several linear control techniques closed loop frequency domain properties such as sensitivities and robustness to small perturbations are usually not taken into account in the mpc design this technical note considers the problem of tuning an mpc controller that behaves as a given linear controller when the constraints are not active e g for perturbations around the equilibrium that remain within the given input and state bounds therefore inheriting the small signal properties of the linear control design and that still optimally deals with constraints during transients we provide two methods for selecting the mpc weight matrices so that the resulting mpc controller behaves as the given linear controller therefore solving the posed inverse problem of controller matching and is globally asymptotically stable

new solution to the inverse regulator problem by the polynomial matrix method abstract this paper gives a new criterion for the inverse regulator problem in terms of polynomial matrix fractions the generalized kalman equation in polynomial matrix form leads to a necessary and sufficient condition for a stable feedback law to be optimal for some unknown quadratic performance index this criterion consists of i a symmetric factorizability of a polynomial matrix and ii a polynomial type criterion that guarantees detectability the relationship between the riccati and kalman equations is also established finally an example is given to illustrate the new result in contrast with the existing result

solving multicommodity flow problems by an approximation scheme we study an approximation scheme to solve minimum cost multicommodity flow problems to a relative accuracy of varepsilon in 0 1 the proposed scheme which we shall call algorithm cal a is a bisection based procedure so it maintains an interval that contains the optimal value at each iteration algorithm cal a defines a block angular sharing problem that is solved to a relative accuracy of o varepsilon the computed solution defines the current approximation to an optimal solution and it is used by algorithm cal a to throw away half of the current interval it is shown that when algorithm cal a no longer shrinks the current interval the current solution solves the minimum cost multicommodity flow problem to the given accuracy varepsilon to compute approximate solutions to the sharing problems that algorithm cal a defines we propose using algorithm cal l from j villavicencio and m d grigoriadis approximate lagrangian decomposition with a modified karmarkar logarithmic potential in network optimization lecture notes in econom and math systems 450 springer berlin 1997 pp 471 485 but we replace its fixed small step size by one computed using inexact line searches this modification allows large steps in algorithm cal l we show that the coordination complexities of algorithm cal l and algorithm cal l with inexact line searches are the same if these algorithms are applied to the block angular sharing problems defined by algorithm cal a this result is also true for block angular sharing problems with convex blocks and with coupling constraints given by nonnegative linear functions

optimal distributed kalman filtering fusion with singular covariances of filtering errors and measurement noises in this paper we present the globally optimal distributed kalman filtering fusion with singular covariances of filtering errors and measurement noises the following facts motivate us to consider the problem first the invertibility of estimation error covariance matrices is a necessary condition for most of the existing distributed fusion algorithms however it can not be guaranteed to exist in practice for example when state estimation for a given dynamic system is subject to state equality constraints the estimation error covariance matrices must be singular second the proposed fused state estimate is still exactly the same as the centralized kalman filtering using all sensor raw measurements moreover the existing performance analysis results on the distributed kalman filtering fusion for the multisensor system with feedback are also extended to the singular covariance matrices of filtering error the final numerical examples support the theoretical results and show an advantage of less computational burden

some results on linear equality constrained state filtering this paper addresses the linear equality constrained state filtering for linear dynamic systems from different perspectives first by integrating constraint information into the state equation to ensure that the estimates naturally satisfy the constraints the constrained filtering problem can be transformed into an unconstrained one second according to a linear transformation of the state vector and the linear relationship between different new state components a reduced order kalman filter is developed third adding a projection step after the one step state prediction in the kalman filtering algorithm we present a state prediction projection method these approaches are mutually equivalent and the existing null space method proves to be a special case of them most of current methods and the proposed approaches can be summed up in a unified framework and boil down to three forms of the projection method finally a vehicle tracking example is provided to compare the performance of the discussed

the inverse problem of linear optimal control for constant disturbance this paper presents the solution to the inverse problem of linear optimal control systems to achieve pole placement and at the same time minimize the cost function and accommodate a constant but unknown disturbance the sufficient conditions for an optimal feedback law to have a positive r and positive semi definite q are found the relationships between the open loop poles and the closed loop poles that guarantee a positive r and q 0 are also obtained these relations offer a rule for selection of the appropriate closed loop poles which will guarantee the required feedback properties

a note on a sufficient decrease criterion for a non derivative step length procedure a step length algorithm is an essential part of many descent methods for unconstrained and constrained optimization in this note we present a criterion that defines an acceptable step length when only function values are available at trial step lengths

stopping criteria for linesearch methods without derivatives in this paper acceptability criteria for the linesearch stepsize are introduced which require only function values simple algorithm models based on these criteria are presented some modifications of criteria based on the knowledge of the directional derivative are also illustrated

state estimation with probability constraints this paper considers a state estimation problem for a discrete time linear system driven by a gaussian random process the second order statistics of the input process and state initial condition are uncertain however the probability that the state and input satisfy linear constraints during the estimation interval is known a minimax estimation problem is formulated to determine an estimator that minimises the worst case mean square error criterion over the uncertain second order statistics subject to the probability constraints it is shown that a solution to this constrained state estimation problem is given by a kalman filter for appropriately chosen input and initial condition models these models are obtained from a finite dimensional convex optimisation problem the application of this estimator to an aircraft tracking problem quantifies the improvement in estimation accuracy obtained from the inclusion of probability constraints in the minimax formulation

on the use of constraints in least squares estimation and control in this article we examine the effect of constraints on estimation and control methods based on quadratic penalty functions we begin with estimation theory and analyze how constraints alter the statistical properties of the least squares estimates it is shown that constraints can be used to formulate maximum likelihood mle and maximum a posteriori map estimators for a variety of unimodal distributions this provides greater flexibility over the assumption of normality inherent in the mle and map interpretation of traditional least squares we discuss how these ideas apply to state space models of dynamic systems possible applications for controllers that handle constraints are also discussed a parameter estimation example is given to demonstrate the potential for improved performance over unconstrained least squares

adaptive beamforming using the constrained kalman filter from the viewpoint of achieving rapid convergence application of a kalman filter to an adaptive array is considered compared with the frost s 1972 constrained least mean square algorithm the constrained kalman algorithm for adaptive beamforming is proposed to overcome the problem of signal distortion along the look direction which occurs in the unconstrained kalman beamformer of baird 1974 a constraint on the array response along the look direction is added to the measurement equation of the kalman filter the weight vector of the constrained kalman beamformer is derived and shown to converge to that of the minimum variance distortionless response beamformer the convergence rate of the proposed algorithm is also analyzed compared to baird s algorithm and the sidelobe canceller with one step kalman predictor simulation results show the effectiveness of the proposed algorithm

comment on a new method for the nonlinear transformation of means and covariances in filters and estimators with authors reply the above paper julier et al ieee trans automat contr vol 45 pp 477 82 2000 generalizes the kalman filter to nonlinear systems by transforming approximations of the probability distributions through the nonlinear process and measurement functions this comment derives exactly the same estimator by linearizing the process and measurement functions by a statistical linear regression through some regression points in contrast with the extended kalman filter which uses an analytic linearization in one point this insight allows one 1 to understand predict the performance of the estimator for specific applications and 2 to make adaptations to the estimator i e the choice of the regression points and their weights in those cases where the original formulation does not assure good results in reply the authors state that the commenters conclusion is unnecessarily narrow interpretation of results

design of linear quadratic regulators with assigned eigenstructure a recursive design procedure is presented which assigns the closed loop eigenstructure in linear quadratic regulators at each stage the required solution for the steady state riccati matrix which shifts a pole or pole pair to specified values is obtained for pole pair placement a free parameter in the solution permits selection of closed loop eigenvectors the interactive design procedure is summarized and illustrated by an example

kalman filtering for general discrete time linear systems recursive state estimation problems for explicit and implicit time invariant linear systems both for systems with and without unknown inputs can be formulated as a single problem usually referred to as descriptor kalman filtering solutions to this problem have been proposed in the literature however these solutions either neglect possible contributions of future dynamics to the current estimate or make unnecessary assumptions on the structure of the system in this paper the authors propose a solution to this problem which leads to a constructive method lifting these unnecessary assumptions this method uses a generalization of the shuffle algorithm

gain constrained kalman filtering for linear and nonlinear systems this paper considers the state estimation problem with a constraint on the data injection gain special cases of this problem include the enforcing of a linear equality constraint in the state vector the enforcing of unbiased estimation for systems with unknown inputs and simplification of the estimator structure for large scale systems both the one step gain constrained kalman predictor and the two step gain constrained kalman filter are presented the latter is extended to the nonlinear case yielding the gain constrained unscented kalman filter two illustrative examples are presented

on successive pole assignment by linear quadratic optimal feedbacks abstract this paper studies a method of shifting poles of linear constant systems via lq optimal feedback by making use of a solution to the so called inverse regulator problem this method enables us to shift poles successively by pairs while maintaining the well known advantages of lq regulators polynomial fractional representation is effectively used both to characterize the maximal pole assignable area which clarifies the theoretical bound of the lq optimal pole shifting and to derive an algorithm a numerical example is given to illustrate the results

a new method for the nonlinear transformation of means and covariances in filters and estimators this paper describes a new approach for generalizing the kalman filter to nonlinear systems a set of samples are used to parametrize the mean and covariance of a not necessarily gaussian probability distribution the method yields a filter that is more accurate than an extended kalman filter ekf and easier to implement than an ekf or a gauss second order filter its effectiveness is demonstrated using an example

on kalman filtering with nonlinear equality constraints the state space description of some physical systems possess nonlinear equality constraints between some state variables in this paper we consider the problem of applying a kalman filter type estimator in the presence of such constraints we categorize previous approaches into pseudo observation and projection methods and identify two types of constraints those that act on the entire distribution and those that act on the mean of the distribution we argue that the pseudo observation approach enforces neither type of constraint and that the projection method enforces the first type of constraint only we propose a new method that utilizes the projection method twice once to constrain the entire distribution and once to constrain the statistics of the distribution we illustrate these algorithms in a tracking system that uses unit quaternions to encode orientation

using data driven discrete time models and the unscented kalman filter to estimate unobserved variables of nonlinear systems this paper addresses the problem of state estimation for nonlinear systems by means of the unscented kalman filter ukf compared to the traditional extended kalman filter the ukf does not require the local linearization of the system equations used in the propagation stage important results using the ukf have been reported recently but in every case the system equations used by the filter were considered known not only that such models are usually considered to be differential equations which requires that numerical integration be performed during the propagation phase of the filter in this paper the dynamical equations of the system are taken to be difference equations thus avoiding numerical integration and are built from data without prior knowledge the identified models are subsequently implemented in the filter in order to accomplish state estimation the paper discusses the impact of not knowing the exact equations and using data driven models in the context of state and joint state and parameter estimation the procedure is illustrated by means of examples that use simulated and measured data

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

constrained state estimation for nonlinear discrete time systems stability and moving horizon approximations state estimator design for a nonlinear discrete time system is a challenging problem further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances one strategy for constrained state estimation is to employ online optimization using a moving horizon approximation we propose a general theory for constrained moving horizon estimation sufficient conditions for asymptotic and bounded stability are established we apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation examples are used to illustrate the benefits of constrained state estimation our framework is deterministic

a complete optimality condition in the inverse problem of optimal control a complete optimality condition in the standard inverse problem of optimal control for the multi input case is established the optimality of a feedback control law is characterized completely in terms of a new geometric condition as well as the well known return difference condition the new condition not only provides a better insight into the well known sensitivity reduction property of optimal control for the multi input case but also indicates an essential difference between the solutions of the single and multi input inverse problem

partial pole placement by lq regulators an inverse problem approach this paper gives a necessary and sufficient condition under which a state feedback control law places part of the closed loop poles exactly at specified points and at the same time is linear quadratic optimal for some quadratic weightings this is made possible by means of a solution to the inverse problem of optimal control a design example is given to illustrate the result

modeling and state estimation for dynamic systems with linear equality constraints the problem of modeling and estimation for linear equality constrained lec systems is considered the exact constrained dynamic model usually is not readily available or is too complicated and hence in many studies an auxiliary dynamic model is employed in which the state does not necessarily obey the constraint strictly based on the understanding that the constraints as prior information about the state should be incorporated into the dynamics modeling an lec dynamic model lecdm is constructed first the model optimally fuses the linear equality constraint lec and the auxiliary dynamics some of its superior properties are presented next the linear minimum mean squared error lmmse estimate of the lec state is proved to satisfy the constraint the lmmse estimator for linear systems called the lec kalman filter leckf and two approximate lmmse estimators for nonlinear systems are presented the leckf is compared with other constrained estimators and a sufficient condition is also provided under which the estimate projection method mathematically equals the leckf furthermore extensions of the lecdm for the lec systems with uncertain or unknown constraint parameters are discussed finally illustrative examples are provided to show the effectiveness and efficiency of the leckf and to verify the theoretical results given in the paper

a new approach to the lq design from the viewpoint of the inverse regulator problem a new design method of lq regulators is developed by reverse application of pertinent results on the inverse regulator problem the lq regulator of interest here is unlike the usual one designed without specifying a quadratic cost but it proves to minimize some quadratic cost hence it possesses those well known robustness properties shared by all lq regulators a basic design procedure is developed first and followed by practical ones in which the design parameters are chosen based on asymptotic modal properties of the regulator this new method requires no riccati solutions thereby leading to simplification of the lq design as compared to the usual one