Adaptive sliding mode control for interval type-2 stochastic fuzzy systems subject to actuator failures

Abstract

This paper investigates the problem of adaptive sliding mode control for a class of interval type-2 Itô stochastic fuzzy systems, where the actuator failures may happen. The sliding function is firstly constructed, whose key feature is its dependence on the upper membership functions. And then, an adaptive scheme is proposed to estimate the effectiveness lose values of faulty actuators, and a sliding mode controller based on estimating scheme is designed such that the reachability of the specified sliding surface can be guaranteed even in the presence of actuator failures, in which the lower and upper membership functions are involved. Moreover, the stability conditions of sliding mode dynamics are derived, which involve some coupling terms of Lyapunov matrix and the sliding matrix. By introducing additional matrix variables and employing the cone complementary linearisation algorithm, the above nonlinear stability criterions are decoupled and lastly converted to a minimisation problem with linear constraints. Finally, a numerical example demonstrates the validity of the proposed method.