Adaptive Synchronization of Uncertain Fractional-order Chaotic Systems Based on Projective Method

Based on the stability theory of fractional-order system and Lyapunov stability theory, and using the sliding mode adaptive control and projective method, a synchronization control strategy is proposed for a class of fractional-order chaotic systems with uncertain parameters, uncertain nonlinear functions and external disturbances. A stable fractional-order integral sliding surface is selected and the adaptive laws are designed to estimate the uncertainties, consequently, the synchronization controller is obtained. Then, the projective method is introduced to modify above basic adaptive laws to prevent the adaptive parameters from diverging to infinite, thus, the boundedness of the control inputs is guaranteed. Finally, the numerical simulation result is presented to show the effectiveness and applicability of the proposed control strategy.