This study introduces a mixed H/sub 2//H/sub /spl infin// fuzzy output feedback control design method for nonlinear systems with guaranteed control performance. First, the Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based mixed H/sub 2//H/sub /spl infin// controller is developed to achieve the suboptimal H/sub 2/ control performance with a desired H/sub /spl infin// disturbance rejection constraint. A robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure. By the proposed decoupling technique and two-stage procedure, the outcome of the fuzzy observer-based mixed H/sub 2//H/sub /spl infin// control problem is parametrized in terms of the two eigenvalue problems (EVPs): one for observer and the other for controller. The EVPs can be solved very efficiently using the linear matrix inequality (LMI) optimization techniques. A simulation example is given to illustrate the design procedures and performances of the proposed method.

Mixed H/sub 2//H/sub /spl infin// fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach

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

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

Multi-player non-zero-sum games: Online adaptive learning solution of coupled Hamilton-Jacobi equations

This paper discusses the $H_{\infty}$ control problem for a class of nonlinear stochastic systems with both state- and disturbance-dependent noise. By means of Hamilton--Jacobi equations, both infinite and finite horizon nonlinear stochastic $H_\infty$ control designs are developed.
Some results on nonlinear $H_\infty$ control of deterministic systems are generalized to a stochastic setting. We introduce some useful concepts such as "zero-state observability" and "zero-state detectability" which, together with the stochastic LaSalle invariance principle, yield some valuable consequences in infinite horizon nonlinear stochastic $H_\infty$ control.

State Feedback $H_\infty$ Control for a Class of Nonlinear Stochastic Systems

In this paper, we aim to study the observer design problem for polytopic linear-parameter-varying (LPV) systems with uncertain measurements on scheduling variables. Due to the uncertain measurements, the uncertainties are considered in the weighting factors. It is assumed that the vertices of polytope are the same when the measurements on scheduling variables are uncertain and perfect. Then, an LPV system with the uncertain weighting factors can be transferred to an LPV system with uncertainties. To deal with the uncertainties and unknown disturbance in the observer design problem, we propose a gain-scheduling sliding mode observer. Defining the estimation error as the state vector minus the estimated state vector, the estimation error dynamics is established. The sliding mode observer design method is developed based on analysis results of the established estimation error system. The proposed observer design method is then applied to an electric ground vehicle (EGV) in which the measurement of longitudinal velocity is assumed to be uncertain. Experimental tests and comparisons are given to show the advantages of the proposed design method and the designed observer.

$\mathcal{H}_{\infty}$ Observer Design for LPV Systems With Uncertain Measurements on Scheduling Variables: Application to an Electric Ground Vehicle

The established theory of nonzero sum games is used to solve a mixed H/sub 2//H/sub /spl infin//, control problem. Our idea is to use the two pay-off functions associated with a two-player Nash game to represent the H/sub 2/ and H/sub /spl infin// criteria separately. We treat the state-feedback problem and we find necessary and sufficient conditions for the existence of a solution. Both the finite and infinite time problems are considered. In the infinite horizon case we present a full stability analysis. The resulting controller is a constant state-feedback law, characterized by the solution to a pair of cross-coupled Riccati equations, which may be solved using a standard numerical integration procedure. We begin our development by considering strategy sets containing linear controllers only. At the end of the paper we broaden the strategy sets to include a class of nonlinear controls. It turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers. >

A Nash game approach to mixed H/sub 2//H/sub /spl infin// control

The established theory of non-zero sum games is used to solve a mixed H 2/H ∞ control problem. Our idea is to use the two pay-off functions associated with a two player Nash game to represent the H 2 and H ∞ criteria separately. We treat the state feedback problem, and we find necessary and sufficient conditions for the existence of a solution. A full stability analysis is available in the infinite horizon case [13], and the resulting controller is a constant state feedback law which is characterised by the solution to a pair of cross-coupled Riccati differential equations.

Nash games and mixed H2/H∞ control

The aim of this paper is to study an H 2/H ∞ terminal state estimation problem using the classical theory of Nash equilibria. The H 2/H ∞ nature of the problem comes from the fact that we seek an estimator which satisfies two Nash inequalities. The first reflects an H ∞ filtering requirement in the sense alluded to in [4], while the second inequality demands that the estimator be optimal in the sense of minimising the variance of the terminal state estimation error. The problem solution exploits a duality with the H 2/H ∞ control problem studied in [2, 3]. By exploiting duality in this way, one may quickly extablish that an estimator exists which staisfies the two Nash inequalities if and only if a certain pair of cross coupled Riccati equations has a solution on some optimisation interval. We conclude the paper by showing that the Kalman filtering, H ∞ filtering and H 2/H ∞ filtering problems may all be captured within a unifying Nash game theoretic framework.

B. Hendel

Papers

A Nash game approach to mixed H/sub 2//H/sub /spl infin// control

Nash games and mixed H2/H∞ control

Mixed H2/H∞ filtering by the theory of nash games