A Fractional Adaptive Sliding Mode Control Configuration for Synchronizing Disturbed Fractional-Order Chaotic Systems

In the two last decades, several research works proposed adaptive sliding mode control (SMC) algorithms to deal with fractional-order chaotic systems for control and synchronization. As a contribution to this investigation effort, this paper proposes a new adaptation law for fractional-order SMC addressing the synchronization problem for a class of nonlinear fractional-order systems with chaotic behavior. The main innovation in the proposed control design concerns the choice of a sliding surface with two adjustable parameters, leading easily to an efficient adaptation law for the SMC controller. Stability analysis of the proposed control scheme is performed using the Lyapunov stability theorem. As an illustration of the effectiveness of this synchronization strategy, a simulation example on the fractional-order Arneodo chaotic system is presented and discussed.