Synchronization of fractional-order chaotic systems based on adaptive fuzzy control

Abstract

In this paper the synchronization problem for fractional-order chaotic system with unknown external disturbance is investigated by adaptive fuzzy control. Based on the fractional Lyapunov stability theorem, an adaptive fuzzy controller, which is accompanied with fractional adaptation law, is established. Fuzzy logic system is used to approximate an unknown nonlinear function. The fuzzy approximation error can be canceled by the proposed fractional adaptation law. Just like the stability analysis in an integer-order chaotic system, the quadratic Lyapunov function is used to analyze the stability of the fractional-order closed-loop system. The control method can realize good synchronization performances between two fractional-order chaotic systems, and the synchronization error tends to zero asymptotically. Besides, the proposed controller can also guarantee the boundedness of all signals in the closed-loop system. Finally, the numerical simulation results illustrate the effectiveness of the proposed control method for fractional-order chaotic system in the presence of the external disturbances.