Finite-Time Adaptive Sliding Control for a Class of Perturbed MIMO Nonlinear Systems

In this paper, we introduce an adaptive sliding mode control (SMC) to deal with a finite-time convergence problem of a multiple inputs and multiple outputs (MIMO) system in the presence of uncertainties and/or external disturbances. The proposed controller is constructed by using the super-twisting sliding mode technique to eliminate a negative effect of the chattering phenomenon on the system. Additionally, an adaptive law is designed to guarantee a rapid adaptation and robust stability of the closed-loop system even without knowledge of the upper bound conditions of uncertainties/perturbations. The stability of a control system is investigated by the Lyapunov theorem. A great efficiency of the proposed algorithm is proven through a numerical simulation of a chaotic system.