An optimal robust fuzzy adaptive integral sliding mode controller based upon a multi-objective grey wolf optimization algorithm for a nonlinear uncertain chaotic system

Abstract

This paper presents a novel robust fuzzy adaptive integral sliding mode controller designed via a multi-objective grey wolf optimization algorithm for a nonlinear uncertain chaotic system. To this end, proper integral surfaces are defined and a sliding mode stabilizer is designed to converge the system errors to zero. Next, the gradient descent approach is employed to tune the design gains of the integral sliding mode controller. Then, fuzzy rules are employed to regulate the coefficients of the proposed robust control approach. In order to acquire the proper parameters of the proposed controller and avoid trial-and-error processes, a multi-objective grey wolf optimization algorithm is employed to enhance the performance of the proposed controller. The challenging case study of a Duffing-Holmes oscillator, as a nonlinear autonomous uncertain chaotic system without stable equilibrium points, is considered to assess the behavior of the suggests optimal robust fuzzy adaptive integral sliding mode controller. The results of this study are compared with the outcomes of a distinguished work in the literature. Lastly, the discussions elucidate the efficiency of the proposed controller with respect to uncertain chaotic nonlinear systems in terms of optimal control inputs and minimum tracking error.