A Novel Sliding Mode Synchronization Method of Uncertain Fractional-Order Chaotic Systems

A novel adaptive sliding mode synchronization controller for uncertain fractional order chaotic systems is proposed in this paper. The proposed controller can realize the synchronization of systems with parameters perturbation, function uncertainties, and exterior disturbance. The new sliding mode surface with fractional order has advantages of week chattering and high convergent rate. A novel fractional order adaptive updating law is proposed to prevent the estimations from increasing infinitely. The sliding mode surface and the parameter estimation error of the controller are modelled by utilizing frequency distribution model, and the convergence of the error system is verified by Lyapunov functions, avoiding the mistake caused by directly applying pseudo state variables for the analysis of system synchronization error. Simulation results demonstrate the effectiveness of the proposed scheme.