Adaptive Terminal Sliding-Mode Synchronization Control with Chattering Elimination for a Fractional-Order Chaotic System

In this paper, an adaptive terminal sliding-mode control (ATSMC) method is proposed for the synchronization of uncertain fractional-order chaotic systems with disturbances. According to the sliding-mode control theory, a non-singular sliding surface is constructed. To overcome the chattering problem of ATSMC, a smooth term is used in the controller. In order to reduce the estimation error of an uncertain parameter, adaptive laws are designed to adjust the amplitude of the continuous function. Based on the Lyapunov stability theory, a stability analysis of the error system is performed to ensure that the tracking error eventually converges to the origin. The effectiveness and applicability of the proposed control strategy are verified using the simulation results.