Fixed-order robust H/sub /spl infin// filter design for Markovian jump systems with uncertain switching probabilities

This paper discusses the fixed-order robust H/sub /spl infin// filtering problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration are assumed to be norm-bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix, respectively. First, a criterion based on linear matrix inequalities is provided for testing the H/sub /spl infin// filtering level of a filter over all the admissible uncertainties. Then, a sufficient condition for the existence of the fixed-order robust H/sub /spl infin// filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints. To determine the filter, a globally convergent algorithm involving convex optimization is suggested. Finally, a numerical example is used to illustrate that the developed theory is more effective than the existing results.     

An H/sub /spl infin// optimization and its fast algorithm for time-variant system identification

In some estimation or identification techniques, a forgetting factor /spl rho/ has been used to improve the tracking performance for time-varying systems. However, the value of /spl rho/ has been typically determined empirically, without any evidence of optimality. In our previous work, this open problem is solved using the framework of H/sub /spl infin// optimization. The resultant H/sub /spl infin// filter enables the forgetting factor /spl rho/ to be optimized through a process noise that is determined by the filter Riccati equation. This paper seeks to further explain the previously derived H/sub /spl infin// filter, giving an H/sub /spl infin// interpretation of its tracking capability. Additionally, a fast algorithm of the H/sub /spl infin// filter, called the fast H/sub /spl infin// filter, is presented when the observation matrix has a shifting property. Finally, the effectiveness of the derived fast algorithm is illustrated for time-variant system identification using several computer simulations. Here, the fast H/sub /spl infin// filter is shown to outperform the well known least-mean-square algorithm and the fast Kalman filter in convergence rate.     

Robust H/sub /spl infin// filtering for Uncertain2-D continuous systems

This paper considers the problem of robust H/sub /spl infin// filtering for uncertain two-dimensional (2-D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm-bounded in both the state and measurement equations. The purpose is the design of a 2-D continuous filter such that for all admissible uncertainties, the error system is asymptotically stable, and the H/sub /spl infin// norm of the transfer function, from the noise signal to the estimation error, is below a prespecified level. A sufficient condition for the existence of such filters is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H/sub /spl infin// filter is given. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.     

H/sub /spl infin// filtering for multiple-time-delay measurements

The aim of this paper is to study the H/sub /spl infin// filtering problem for linear continuous-time systems with both current and multiple-time-delay measurements. The key technique applied for deriving the filter is the reorganized innovation analysis approach in Krein space. A necessary and sufficient condition for the existence of an H/sub /spl infin// filter is derived, and the solution to the H/sub /spl infin// filter is given in terms of solutions of Riccati and matrix differential equations. An example is finally presented to show the effectiveness of the proposed approach.     

An LMI approach to the H/sub /spl infin// filter design for uncertain systems with distributed delays

This paper investigates the problem of robust H/sub /spl infin// filter design for linear distributed delay systems with norm-bounded time-varying parameter uncertainties. The distributed delays are assumed to appear in both the state and measurement equations. The problem we address is the design of a filter, such that for all admissible uncertainties, the resulting error system is asymptotically stable and satisfies a prescribed H/sub /spl infin// performance level. A sufficient condition is obtained to guarantee the existence of desired H/sub /spl infin// filters, which can be constructed by solving certain linear matrix inequalities. The effectiveness of the proposed design method is demonstrated by a numerical example.     

Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements

In this paper, the robust H/sub /spl infin// filtering problem is studied for stochastic uncertain discrete time-delay systems with missing measurements. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. We aim to design filters such that, for all possible missing observations and all admissible parameter uncertainties, the filtering error system is exponentially mean-square stable, and the prescribed H/sub /spl infin// performance constraint is met. In terms of certain linear matrix inequalities (LMIs), sufficient conditions for the solvability of the addressed problem are obtained. When these LMIs are feasible, an explicit expression of a desired robust H/sub /spl infin// filter is also given. An optimization problem is subsequently formulated by optimizing the H/sub /spl infin// filtering performances. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.     

Design of reduced-order H/sub /spl infin// filter for Markovian jumping systems with time delay

This brief is concerned with the reduced-order H/sub /spl infin// filtering problem for Markovian jumping linear systems with time delay, where the jumping parameters are modeled by a discrete-time Markov process. Sufficient conditions for the existence of the reduced-order H/sub /spl infin// filter are proposed in terms of linear matrix inequalities (LMI) and a coupling nonconvex matrix rank constraint. In particular, the sufficient conditions for the existence of the zeroth-order (or static) H/sub /spl infin// filter can be expressed in terms of a set of strict LMIs. The explicit parameterization of the desired filter is also given. Finally, a numerical example is given to illustrate the proposed approach.     

Experimental implementation of spatial H/sub /spl infin// control on a piezoelectric-laminate beam

This paper is aimed to develop a feedback controller that suppresses vibration of flexible structures. The controller is designed to minimize the spatial H/sub /spl infin// norm of the closed-loop system. This technique guarantees average reduction of vibration throughout the entire structure. A feedthrough term is incorporated into the truncated flexible-structure model to compensate for the neglected dynamics in the finite-dimensional model. Adding the feedthrough term reduces the uncertainty associated with the truncated model, which is instrumental in ensuring the robustness of the closed-loop system. The controller is applied to a simply-supported piezoelectric-laminate beam and is validated experimentally to show the effectiveness of the proposed controller in suppressing structural vibration. It is shown that the spatial H/sub /spl infin//. control has an advantage over the pointwise H/sub /spl infin// control in minimizing the vibration of the entire structure. This spatial H/sub /spl infin// control methodology can also be applied to more general structural vibration suppression problems.     

Design of Luenberger state observers using fixed-structure H/sub /spl infin// optimization and its application to fault detection in lane-keeping control of automated vehicles

Lane-keeping control forms an integral part of fully automated intelligent vehicle highway systems (IVHS) and its reliable operation is critical to the operation of an automated highway. We present the design of a fault detection filter for the lane-keeping control systems onboard vehicles used by California-PATH, USA in its automated highways program. We use a Luenberger structure for the fault detection filters and tune the observer gains based on an H/sub /spl infin//-based cost. Such a choice of cost was motivated by the need to explicitly incorporate frequency-domain-based performance objectives. The linear matrix inequality (LMI)-based formulation of an H/sub /spl infin// optimization problem of Luenberger state observers does not allow for the augmentation with dynamic performance weightings in the optimization objective, since it makes the problem a nonconvex optimization problem. We present an algorithm to locally solve the problem of the design of Luenberger state observers using H/sub /spl infin// optimization by transforming the problem into an H/sub /spl infin// static output feedback controller problem. Experimental results demonstrate the efficacy of the tuning methodology by comparing the fault detection performance of filters that use H/sub /spl infin// Luenberger observers versus those that use Kalman filters. Implementation issues of the observers are also discussed.     

Robust H/sub /spl infin// controller design with recurrent neural network for linear synchronous motor drive

In this paper, a robust controller design with H/sub /spl infin// performance using a recurrent neural network (RNN) is proposed for the position tracking control of a permanent-magnet linear synchronous motor. The proposed robust H/sub /spl infin// controller, which comprises a RNN and a compensating control, is developed to reduce the influence of parameter variations and external disturbance on system performance. The RNN is adopted to estimate the dynamics of the lumped plant uncertainty, and the compensating controller is used to eliminate the effect of the higher order terms in Taylor series expansion of the minimum approximation error. The tracking performance is ensured in face of parameter variations, external disturbance and RNN estimation error once a prespecified H/sub /spl infin// performance requirement is achieved. The synthesis of the RNN training rules and compensating control are based on the solution of a nonlinear H/sub /spl infin// control problem corresponding to the desired H/sub /spl infin// performance requirement, which is solved via a choice of quadratic storage function. The proposed control method is able to track both the periodic step and sinusoidal commands with improved performance in face of large parameter perturbations and external disturbance.     

H/sub /spl infin// filtering for fuzzy singularly perturbed systems with pole placement constraints: an LMI approach

This paper addresses the problem of designing an H/sub /spl infin// filter for a class of nonlinear singularly perturbed systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a fuzzy H/sub /spl infin// controller that guarantees that i) the L/sub 2/-gain from an exogenous input to a filter error is less than or equal to a prescribed value and ii) the poles of each local filter are within a prespecified region. In order to alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities, which are independent of the singular perturbation /spl epsiv/, when /spl epsiv/ is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones, and it can be applied not only to standard but also to nonstandard singularly perturbed nonlinear systems. A numerical example is provided to illustrate the design developed in this paper.     

Robust H/sub /spl infin// control of singular impulsive systems with uncertain perturbations

This paper discusses the problem of robust H/sub /spl infin// control for singular impulsive uncertain systems. Some new fundamental properties of singular systems with impulse effect are derived. Based on the Riccati inequality approach, sufficient conditions for robust H/sub /spl infin// criteria of the corresponding singular impulsive closed-loop systems are established. A simple approach to the design of a robust impulsive controller is then presented. Finally, a design example and simulation results are given to demonstrate the effectiveness of the proposed approach.     

A delay-dependent approach to robust H/sub /spl infin// filtering for uncertain discrete-time state-delayed systems

A delay-dependent approach to robust H/sub /spl infin// filtering is proposed for linear discrete-time uncertain systems with multiple delays in the state. The uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed H/sub /spl infin// noise attenuation level. The proposed filter design methodology incorporates some recently appeared results, such as Moon's new version of the upper bound for the inner product of two vectors and de Oliveira's idea of parameter-dependent stability, which greatly reduce the overdesign introduced in the derivation process. In addition to the full-order filtering problem, the challenging reduced-order case is also addressed by using different linearization procedures. Both full- and reduced-order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms. Numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies.     

Finite horizon H/sub /spl infin// fixed-lag smoothing for time-varying continuous systems

In this paper, we aim to solve the long-standing H/sub /spl infin// fixed-lag smoothing problem for time-varying continuous systems. By applying a novel innovation analysis approach in an indefinite linear space, a sufficient and necessary condition for the existence of an H/sub /spl infin// fixed-lag smoother is derived. The H/sub /spl infin// smoother is calculated by performing the linear matrix differential equation and the integral equation.     

Improved bounded-real-lemma representation and H/sub /spl infin// control of systems with polytopic uncertainties

This brief concerns the problem of the bounded-real-lemma (BRL) representation and H/sub /spl infin// control of linear systems with real convex polytopic uncertainties. In order to use a parameter-dependent Lyapunov function for a system with polytopic uncertainties, the derivative term for the state, which is in the derivative of the Lyapunov function, is reserved; and free weighting matrices are used to express the relationship between the terms of the system equation. This yields a new linear-matrix-inequality approach to BRL representation. In addition, this method is extended to the design of a state-feedback controller that solves the H/sub /spl infin// control problem. Numerical examples demonstrate that the proposed method is effective and is an improvement over previous ones.     

On discrete-time H/sub /spl infin// fixed-lag smoothing

The H/sub /spl infin// fixed-lag smoothing problem for discrete-time linear systems is considered. It is well known that such a problem can be reformulated as a filtering problem for a suitable augmented system. However, in order to check the solvability of the smoothing problem and compute the relevant gains, one must solve a Riccati equation involving the augmented system matrices, which is an approach that may be inefficient, especially for long lags. In this paper, efficient algorithms are worked out that permit checking of solvability and implementation of the smoother, relying only on the solution of the H/sub /spl infin// filtering Riccati equation. In particular, this provides a fast method to compute the minimum lag guaranteeing a desired attenuation level.     

Low-order H/sub /spl infin// controller design for an active suspension system via LMIs

An application of a new controller order reduction technique with stability and performance preservation based on linear matrix inequality optimization to an active suspension system is presented. In this technique, the rank of the residue matrix of a proper rational approximation of a high-order H/sub /spl infin// controller subject to the H/sub /spl infin//-norm of a frequency-weighted error between the approximated controller and the high-order H/sub /spl infin// controller is minimized. However, because solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with a nuclear-norm that can be reduced to a semidefinite program so that it can be solved efficiently. Application to the active suspension system of the Automatic Laboratory of Grenoble provides a fourth-order controller. The experimental results show that the control specifications are met to a large extent.     

Reduced-order H/sub /spl infin// filtering for stochastic systems

This paper deals with the reduced-order H/sub /spl infin// filtering problem for stochastic systems. Necessary and sufficient conditions are obtained for the existence of solutions to the continuous-time and discrete-time problems in terms of certain linear matrix inequalities (LMIs) and a coupling nonconvex rank constraint condition. Furthermore, when these conditions are feasible, an explicit parametrization of all desired reduced-order filters corresponding to a feasible solution is given. In particular, when the reduced-order filter is restricted to be a static one, then simple conditions expressed by LMIs only without any rank constraints are derived, and a parametrization of all solutions is also given. Finally, an illustrative example is provided to show the effectiveness of the proposed approach.