Robust adaptive tracking for Markovian jump nonlinear systems with unknown nonlinearities

Jin Zhu,Hai-Bo Ji,Bing Wang,Hong-Sheng Xi

doi:10.1155/ddns/2006/92932

Abstract

Robust adaptive tracking problems for a class of Markovian jump parametric-strict-feed-back systems with both parametric uncertainty and unknown nonlinearity are investigated. The unknown nonlinearities considered herein lie within some “bounding functions,” which are assumed to be partially known. By using a stochastic Lyapunov method and backstepping techniques, a parameter adaptive law and a control law were obtained, which guarantee that the tracking error could be within a small neighborhood around the origin in the sense of the fourth moment. Moreover, all signals of the closed-loop system could be globally uniformly ultimately bounded.

Highlights

The passed decades have witnessed substantial research activities in the development of Markovian jump systems, and much effort is directed towards jump linear systems [6]
With many linear problems (Kalman filtering [4, 10] and LQG [2, 3], etc.) solved, more attention is focused on the study of Markovian jump nonlinear systems
A robust adaptive control scheme was obtained by using a stochastic Lyapunov method and backstepping techniques, which guarantees that the closed-loop system is globally uniformly bounded

Summary

Introduction

The passed decades have witnessed substantial research activities in the development of Markovian jump systems, and much effort is directed towards jump linear systems [6]. With many linear problems (Kalman filtering [4, 10] and LQG [2, 3], etc.) solved, more attention is focused on the study of Markovian jump nonlinear systems. Markovian jump nonlinear systems disturbed by Wiener noises (or Brown motion) are becoming the subject of numerous studies in recent years. For this class of jump systems, Mao [5] presents the sufficient condition to ensure existence and uniqueness of the solution; Yuan and Mao [11, 12] introduce the notions of stochastic stability. We are interested in the robust adaptive tracking problem for a class of Markovian jump parametric-strict-feedback systems with unknown nonlinearity.

Problem and preliminaries

Control design

Example

Conclusion