A Parameter-Dependent Sliding Mode Approach for Finite-Time Bounded Control of Uncertain Stochastic Systems With Randomly Varying Actuator Faults and Its Application to a Parallel Active Suspension System

Abstract

This paper addresses the mean-square finite-time bounded control problem for uncertain stochastic systems via a sliding mode approach. The stochastic phenomena of randomly occurring uncertainties and randomly varying actuator faults modeled by two independent exponential distributions are addressed effectively. A key issue for the system under the consideration is how to ensure, for any prescribed finite (possibly short ) working time interval, the stochastic finite-time boundedness (SFTB) of the resultant closed-loop systems and the reachability of the specified sliding surface in mean-square sense. To this end, a parameter-dependent sliding mode control (SMC) law is designed to force ( with probability one ) the state trajectories into a domain around the specified sliding surface during the given finite-time interval. The upper bound of the sliding domain associated with the design parameters is obtained explicitly. The sufficient conditions are established, respectively, for guaranteeing the SFTB of the SMC systems over both reaching phase and sliding motion phase . Finally, the proposed finite-time SMC approach is illustrated via a parallel active suspension system.