Robust H/sub /spl infin// static output feedback control of fuzzy systems: an ILMI approach

This paper examines the problem of robust H/sub /spl infin// static output feedback control of a Takagi-Sugeno fuzzy system. The proposed robust H/sub /spl infin// static output feedback controller guarantees the L/sub 2/ gain of the mapping from the exogenous disturbances to the regulated output to be less than or equal to a prescribed level. The existence of a robust H/sub /spl infin// static output feedback control is given in terms of the solvability of bilinear matrix inequalities. An iterative algorithm based on the linear matrix inequality is developed to compute robust H/sub /spl infin// static output feedback gains. To reduce the conservatism of the design, the structural information of membership function characteristics is incorporated. A numerical example is used to illustrate the validity of the design methodologies.     

Fault detection in a mixed H/sub 2//H/sub /spl infin// setting

In this note, we study the problem of fault detection in linear time-invariant (LTI) systems which are simultaneously effected by two classes of unknown inputs: Noises having fixed spectral densities and unknown finite energy disturbances. This problem is formulated as a mixed H/sub 2//H/sub /spl infin// filtering problem. Necessary and sufficient conditions for local optimality are presented. Moreover, it is shown that suboptimal solutions can be computed by solving a convex minimization problem with a set of linear matrix inequality (LMI) constrains. A numerical example is given to illustrate the advantage of the mixed H/sub 2//H/sub /spl infin// approach as compared to existing techniques which are based on optimization of H/sub 2/ and H/sub /spl infin// criteria.     

An innovation approach to H/sub /spl infin// fixed-lag smoothing for continuous time-varying systems

This note studies the finite horizon H/sub /spl infin// fixed-lag smoothing problem for linear continuous time-varying systems. A technique named as reorganized innovation analysis in Krein space is developed to give a necessary and sufficient condition for the existence of an H/sub /spl infin// fixed-lag smoother. The condition is given in terms of the boundedness of two matrix functions which are derived from the solutions of two Riccati differential equations (RDEs), one standard H/sub /spl infin// filtering RDE and one H/sub 2/ type of RDE. Examples demonstrate the proposed H/sub /spl infin// fixed-lag smoother design and the fact that the existence of an H/sub /spl infin// smoother does not depend on the solvability of H/sub /spl infin// filtering.     

Sufficient LMI conditions for H/sub /spl infin// output feedback stabilization of linear discrete-time systems

In this note, sufficient conditions for H/sub /spl infin// output feedback stabilization of linear discrete-time systems are proposed via linear matrix inequalities (LMIs). In order to reduce conservatism existing in earlier LMI methods, auxiliary slack variables with structure are employed. It is shown that degree of freedoms by the introduction of auxiliary slack variables lead to more flexibility in obtaining an approximate solution of H/sub /spl infin// output feedback stabilization problems. Consequently, the proposed method can yield a less conservative result than earlier LMI methods. In particular, typical output feedback control problems, such as decentralized H/sub /spl infin// output feedback control and simultaneous H/sub /spl infin// output feedback control, can be more efficiently solved. Numerical examples are included to illustrate the advantages of the proposed LMI method.     

Stochastic H/sub 2//H/sub /spl infin// control with state-dependent noise

This paper discusses the stochastic H/sub 2//H/sub /spl infin// control problem with state-dependent noise. By means of the stabilization, exact observability and stochastic detectability of stochastic systems, the infinite horizon stochastic H/sub 2//H/sub /spl infin// control design is developed. For the finite horizon H/sub 2//H/sub /spl infin// control problem, our results generalize the corresponding deterministic ones to the stochastic models. Finally, the observer-based suboptimal stochastic H/sub 2//H/sub /spl infin// control is discussed in which the state variables cannot be measured directly, and a feasible design algorithm is proposed.     

New results on delay-dependent control of time-delay systems

This note presents new results pertaining to the delay-dependent stability and control design of a class of linear time-delay systems. A new state transformation is introduced to exhibit the delay-dependent dynamics. For stability, we construct an appropriate Lyapunov functional to derive delay-dependent linear matrix inequality-based sufficient condition. For the feedback control design, we establish schemes based on quadratic H/sub 2/ performance, H/sub /spl infin//, criteria and simultaneous H/sub 2//H/sub /spl infin// synthesis. Under the developed transformation, both the instantaneous and delayed feedback control yield identical results. Numerical examples are presented to illustrate the analytical development.     

Robust H/sub /spl infin// control for fuzzy systems with Frobenius norm-bounded uncertainties

In this paper, we investigate the problem of robust H/sub /spl infin// performance and stabilization for a class of uncertain fuzzy systems with Frobenius norm-bounded parameter uncertainties in all system matrices. Both continuous- and discrete-time uncertain fuzzy systems are considered under a unified treatment called bounded real lemma for fuzzy systems. Unlike the bounded real lemma in the linear theory of robust H/sub /spl infin// control where necessary and sufficient conditions were obtained, only sufficient condition based on Lyapunov method is shown. Furthermore, connection between robust H/sub /spl infin// problems involving uncertainty and standard uncertainty-free H/sub /spl infin// problems is established via matrix algebra. As for controller synthesis, a state feedback fuzzy control law is designed via relaxed linear matrix inequality (LMI) formulations.     

Approaches to quadratic stability conditions and H/sub /spl infin// control designs for T-S fuzzy systems

In this paper, the problems of quadratic stability conditions and H/sub /spl infin// control designs for Takagi-Sugeno (T-S) fuzzy systems have been studied. First, a new quadratic stability condition, which is more simple than that in a previous paper, has been proposed. Second, two new sufficient conditions in the terms of linear matrix inequalities (LMIs) which guarantee the existence of the state feedback H/sub /spl infin// control for the T-S fuzzy systems have been proposed. The conditions are not only simple but also consider the interactions among the fuzzy subsystems. Finally, based on the LMIs, the H/sub /spl infin// controller designing methods for the T-S fuzzy systems have been given.     

Robust H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// filters for equalization designs of nonlinear communication systems: fuzzy interpolation approach

Generally, it is difficult to design equalizers for signal reconstruction of nonlinear communication channels with uncertain noises. In this paper, we propose the H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// filters for equalization/detection of nonlinear channels using fuzzy interpolation and linear matrix inequality (LMI) techniques. First, the signal transmission system is described as a state-space model and the input signal is embedded in the state vector such that the signal reconstruction (estimation) design becomes a nonlinear state estimation problem. Then, the Takagi-Sugeno fuzzy linear model is applied to interpolate the nonlinear channel at different operation points through membership functions. Since the statistics of noises are unknown, the fuzzy H/sub /spl infin// equalizer is proposed to treat the state estimation problem from the worst case (robust) point of view. When the statistics of noises are uncertain but with some nominal (or average) information available, the mixed H/sub 2//H/sub /spl infin// equalizer is employed to take the advantage of both H/sub 2/ optimal performance with nominal statistics of noises and the H/sub /spl infin// robustness performance against the statistical uncertainty of noises. Using the LMI approach, the fuzzy H/sub 2//H/sub /spl infin// equalizer/detector design problem is characterized as an eigenvalue problem (EVP). The EVP can be solved efficiently with convex optimization techniques.     

Fuzzy H/sub /spl infin// output feedback control design for singularly perturbed systems with pole placement constraints: an LMI approach

This paper examines the problem of designing an H/sub /spl infin// output feedback controller with pole placement constraints for singular perturbed Takagi-Sugeno (TS) fuzzy models. We propose a fuzzy H/sub /spl infin// output feedback controller that not only guarantees the /spl Lscr//sub 2/-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, but also ensures closed-loop poles of each subsystem are in a prespecified linear matrix inequality (LMI) region. In order to alleviate the numerical stiffness caused by the singular perturbation /spl epsiv/, the design technique is formulated in terms of a family of /spl epsiv/-independent linear matrix inequalities. The proposed approach can be applied both standard and nonstandard singularly perturbed nonlinear systems. A numerical example is provided to illustrate the design developed in this paper.     

H/sub /spl infin// controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities

This work presents an H/sub /spl infin// controller design method for fuzzy dynamic systems based on techniques of piecewise smooth Lyapunov functions and bilinear matrix inequalities. It is shown that a piecewise continuous Lyapunov function can be used to establish the global stability with H/sub /spl infin// performance of the resulting closed-loop fuzzy control systems and the control laws can be obtained by solving a set of bilinear matrix inequalities (BMIs). Two examples are given to illustrate the application of the proposed methods.     

Robust H/sub /spl infin// control for uncertain discrete-time-delay fuzzy systems via output feedback controllers

This work investigates the problem of robust output feedback H/sub /spl infin// control for a class of uncertain discrete-time fuzzy systems with time delays. The state-space Takagi-Sugeno fuzzy model with time delays and norm-bounded parameter uncertainties is adopted. The purpose is the design of a full-order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed-loop system and guarantees an H/sub /spl infin// norm bound constraint on disturbance attenuation for all admissible uncertainties. In terms of linear matrix inequalities (LMIs), a sufficient condition for the solvability of this problem is presented. Explicit expressions of a desired output feedback controller are proposed when the given LMIs are feasible. The effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust H/sub /spl infin// control for a class of uncertain nonlinear discrete delay systems.     

An H/sub /spl infin// approach to networked control

In this paper, we study the effect of a network in the feedback loop of a control system. We use a stochastic packet-loss model for the network and note that results for discrete-time linear systems with Markovian jumping parameters can be applied. We measure performance using an H/sub /spl infin// norm and compute this norm via a necessary and sufficient matrix inequality condition. We also derive necessary and sufficient linear matrix inequality (LMI) conditions for the synthesis of the H/sub /spl infin// optimal controller for a discrete-time jump system. Finally, we apply these results to study the effect of communication losses on vehicle control.     

Manufacturing systems: LMI approach

This note deals with the control of production systems that produce many part types with limited capacity. First, a simple model is used to show that the inventory control problem can be solved using modern control theory. A state feedback controller that forces the cumulative production of the system to track precisely the cumulative demand is proposed. The tracking problem is formulated as an H/sub /spl infin// control problem and the synthesis of the gains of the state feedback controller that guarantees the H/sub /spl infin// tracking performance of the equivalent dynamics is done by solving a given set of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness of the developed results. The simple model is then extended to include real facts like inspection and processing times.     

Delay-dependent robust H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering for a class of uncertain nonlinear time-delay systems

This note presents delay-dependent robust H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filter designs for a class of nonlinear systems with multiple time-varying delays in the state and parameter uncertainties residing in a polytope. The nonlinearities are assumed to satisfy global Lipschitz conditions. Attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed noise attenuation level in an H/sub /spl infin// or L/sub 2/-L/sub /spl infin// sense. The admissible 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.     

H/sub /spl infin// filtering for singular systems

This note considers the H/sub /spl infin// filtering problem for linear continuous singular systems. The purpose is the design of a linear filter such that the resulting error system is regular, impulse-free and stable while the closed-loop transfer function from the disturbance to the filtering error output satisfies a prescribed H/sub /spl infin//-norm bound constraint. Without decomposing the original system matrices, a necessary and sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is given. Finally, an illustrative example is presented to demonstrate the applicability of the proposed approach.     

Inverse optimal adaptive control for attitude tracking of spacecraft

The attitude tracking control problem of a rigid spacecraft with external disturbances and an uncertain inertia matrix is addressed using the adaptive control method. The adaptive control laws proposed in this paper are optimal with respect to a family of cost functionals. This is achieved by the inverse optimality approach, without solving the associated Hamilton-Jacobi-Isaacs partial differential (HJIPD) equation directly. The design of the optimal adaptive controllers is separated into two stages by means of integrator backstepping, and a control Lyapunov argument is constructed to show that the inverse optimal adaptive controllers achieve H/sub /spl infin// disturbance attenuation with respect to external disturbances and global asymptotic convergence of tracking errors to zero for disturbances with bounded energy. The convergence of adaptive parameters is also analyzed in terms of invariant manifold. Numerical simulations illustrate the performance of the proposed control algorithms.     

H/sub /spl infin// state-feedback controller design for discrete-time fuzzy systems using fuzzy weighting-dependent Lyapunov functions

For discrete-time Takagi-Sugeno (TS) fuzzy systems, we propose an H/sub /spl infin// state-feedback fuzzy controller associated with a fuzzy weighting-dependent Lyapunov function. The controller, which is designed via parameterized linear matrix inequalities (PLMIs), employs not only the current-time but also the one-step-past information on the time-varying fuzzy weighting functions. Appropriately selecting the structures of variables in the PLMIs allows us to find an LMI formulation as a special case.     

Fuzzy neural network quadratic stabilization output feedback control for biped robots via H/sub /spl infin// approach

A novel fuzzy neural network (FNN) quadratic stabilization output feedback control scheme is proposed for the trajectory tracking problems of biped robots with an FNN nonlinear observer. First, a robust quadratic stabilization FNN nonlinear observer is presented to estimate the joint velocities of a biped robot, in which an H/sub /spl infin// approach and variable structure control (VSC) are embedded to attenuate the effect of external disturbances and parametric uncertainties. After the construction of the FNN nonlinear observer, a quadratic stabilization FNN controller is developed with a robust hybrid control scheme. As the employment of a quadratic stability approach, not only does it afford the possibility of trading off the design between FNN, H/sub /spl infin// optimal control, and VSC, but conservative estimation of the FNN reconstruction error bound is also avoided by considering the system matrix uncertainty separately. It is shown that all signals in the closed-loop control system are bounded.