H∞ Control for Nonlinear Infinite Markov Jump Systems

Yueying Liu,Ting Hou

doi:10.1155/2018/2904521

Abstract

In this paper, we discuss the infinite horizon H∞ control problem for a class of nonlinear stochastic systems with state, control, and disturbance dependent noise. The jumping parameters are modelled as an infinite-state Markov chain. Based on the solvability of a set of coupled Hamilton-Jacobi inequalities (HJIs), the exponential mean square H∞ controller for the considered nonlinear stochastic systems is obtained. A numerical example is given to show the effectiveness of the proposed design method.

Highlights

During the past decades, as one of the most important robust control design, H∞ control has been extensively studied in both theory and practical applications [1]
Stochastic H∞ control was firstly investigated in [3] for Itô systems, where a stochastic bounded real lemma was established in the form of linear matrix inequalities
This paper is concerned with the infinite horizon H∞ control problem for a class of nonlinear stochastic systems with infinite Markov jumps and (x, u, V)-dependent noise

Summary

Introduction

As one of the most important robust control design, H∞ control has been extensively studied in both theory and practical applications [1]. Some papers on stability [25,26,27] and control problems [28, 29] of linear infinite Markov jump systems have appeared. To the best of our knowledge, H∞ control problem for a class of nonlinear stochastic systems with infinite Markov jumps is still unsolved, let alone the case of (x, u, V)-dependent noise. This situation motivates us to carry out the present research. This paper is concerned with the infinite horizon H∞ control problem for a class of nonlinear stochastic systems with infinite Markov jumps and (x, u, V)-dependent noise.

Preliminaries

Conclusion