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Adaptive terminal sliding mode synchronization for uncertain fractional-order chaotic systems with disturbance

In this paper, we propose an adaptive terminal sliding mode control method for the synchronization of uncertain fractional-order chaotic system with disturbance. Firstly, a new fractional-order non-singular terminal sliding mode (FO-NTSM) surface with strong robustness is designed to guarantee finite-time convergence to the equilibrium of the error dynamics in the sliding mode. Secondly, an adaptive sliding controller is proposed for synchronizing the fractional-order chaotic systems with retaining the nonlinear part. Thirdly, for the case that the bounds of uncertainties and external disturbances are assumed to be unknown in advance, an adaptive control law is proposed to estimate the unknown bounds online, and force the trajectory of the synchronization error system on the sliding surface. Finally, numerical simulations on synchronizing Chen chaotic system and hyperchaotic Lorenz are carried out separately. The simulation results show the effectiveness and feasibility of the adaptive terminal sliding mode controller.