Two methods for terminal sliding-mode synchronization of fractional-order nonlinear chaotic systems

The self-adaptive terminal sliding mode synchronization of fractional-order nonlinear chaotic systems is investigated under uncertainty and external disturbance. A novel non-singular terminal sliding surface is proposed and proved to be stable. Based on Lyapunov stability theory, a sliding mode control law is proposed to ensure the occurrence of sliding-mode motion. In addition, two methods of the controller and the self-adaptive rules are used to establish the sliding mode function, and two sufficient conditions for achieving self-adaptive terminal sliding-mode synchronization of fractional-order uncertain nonlinear systems are identified. The results show that designing appropriate control law and sliding-mode surface can achieve self-adaptive terminal sliding mode synchronization of the fractional high-order systems with uncertainty. The effectiveness and applicability of the sliding mode control technique are validated through numerical simulation.