Sliding Mode Control of One-Sided Lipschitz Nonlinear Markovian Jump Systems With Partially Unknown Transition Rates

Yuan Li,Yang Liu,Qingdong Sun,Junchao Ren

doi:10.1109/access.2020.3020323

Abstract

This paper investigates the problem of sliding mode control (SMC) for one-sided Lipschitz (OSL) nonlinear Markovian jump systems with partially unknown transition rates. Unmatched norm-bounded uncertainties of state matrices and output matrices are considered. First, a suitable integral-type sliding surface is proposed and a sufficient condition is given such that the sliding mode dynamics is stochastically stable with an H ∞ performance level γ. Next, an SMC law is synthesized such that reachability of the specified sliding surface can be ensured. Finally, two simulation examples are provided to prove the effectiveness of the proposed approach.

Highlights

It is well known that most practical systems are nonlinear, so it is important to design controllers or observers for nonlinear systems
To the best of author’s knowledge, the SMC design method has been widely applied for many kinds of systems, no one has studied the design of sliding mode controller for one-sided Lipschitz (OSL) nonlinear Markovian jump systems with partially unknown transition rates, not to men
Motivated by the above discussion, this paper study the problem of H∞-SMC for OSL nonlinear Markovian jump systems with partially unknown transition rates subject to unmatched uncertainties, external disturbances, and OSL nonlinearities

Summary

INTRODUCTION

It is well known that most practical systems are nonlinear, so it is important to design controllers or observers for nonlinear systems. The problem of H∞-integral sliding mode control for OSL nonlinear systems subject to unmatched uncertainties, external disturbances, and nonlinearities is discussed in [28]. To the best of author’s knowledge, the SMC design method has been widely applied for many kinds of systems, no one has studied the design of sliding mode controller for OSL nonlinear Markovian jump systems with partially unknown transition rates, not to men-. Motivated by the above discussion, this paper study the problem of H∞-SMC for OSL nonlinear Markovian jump systems with partially unknown transition rates subject to unmatched uncertainties, external disturbances, and OSL nonlinearities. The main contributions in this paper are summarised as follows: (i) The problem of H∞-SMC for OSL nonlinear Markovian jump systems with partially unknown transition rates is unavailable in the literature and is addressed for the first time.

SYSTEM REPRESENTATION AND PRELIMINARIES

SLIDING SURFACE DESIGN

SMC LAW SYNTHESIS

ILLUSTRATIVE EXAMPLES

CONCLUSION