Fuzzy Adaptive Controller for Synchronization of Uncertain Fractional-Order Chaotic Systems

Abstract

In this chapter, the projective synchronization problem of different multivariable fractional-order chaotic systems with both uncertain dynamics and external disturbances is studied. More specifically, a fuzzy adaptive controller is investigated for achieving a projective synchronization of uncertain fractional-order chaotic systems. The adaptive fuzzy-logic system is used to online estimate the uncertain nonlinear functions. The latter is augmented by a robust control term to efficiently compensate for the unavoidable fuzzy approximation errors, external disturbances as well as residual error due to the use of the so-called e-modification in the adaptive laws. A Lyapunov approach is employed to derive the parameter adaptation laws and to prove the boundedness of all signals of the closed-loop system. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.