Adaptive Sliding-Mode Control of Markov Jump Nonlinear Systems With Actuator Faults

This technical note is concerned with the design problem of adaptive sliding-mode stabilization for Markov jump nonlinear systems with actuator faults. The specific information including bounds of actuator faults, bounds of the nonlinear term and the external disturbance is not available for the controller design. The main attention focuses on designing the adaptive sliding-mode controller to overcome these problems. Firstly, a sliding-mode surface is constructed such that the reduced-order equivalent sliding motion is stochastically stable. Secondly, the adaptive sliding-mode controller can drive the state trajectories of the system onto the sliding-mode surface in finite time, and can estimate the loss of effectiveness of actuator faults and bounds of the nonlinear term and the external disturbance online. Thirdly, the stochastic stability of the closed-loop system can be guaranteed. Finally, a practical example is provided to demonstrate the effectiveness of the presented results.

I. Introduction

Sliding-mode control (SMC) is a series of variable structure control, whose main feature is its insensitiveness to variations in system parameters and external disturbance. Over the past years, the SMC algorithm has been widely studied [1]–[8]. In recent years, SMC approach has been extended to Markov jump systems (MJSs) in [9]–[13]. In [9], the problem of SMC for stochastic MJSs with actuator degradation was considered. A sliding-mode controller was designed for linear systems with Markov jumping parameters in [10]. In [13], the problems of stochastic stability and SMC for a class of linear continuous-time MJSs were investigated.