Backstepping-Based Adaptive Fuzzy Synchronization Control for a Class of Fractional-Order Chaotic Systems with Input Saturation

In existing backstepping control schemes of fractional-order systems, either using the optional control method or ignoring the fractional-order derivatives of command functions as the analytic calculation of virtual controllers makes the operation becoming prohibitive. This paper proposes an adaptive fuzzy backstepping synchronization control method for a class of factional-order chaotic systems with input saturation and unknown external disturbance, where the fractional-order derivative of the virtual control function is treated as a part of an unknown function. During the backstepping design, the unknown function is approximated by a fuzzy logic system in each step. Then, by using the fractional Lyapunov stability criterion, asymptomatic convergence of the synchronization error can be guaranteed by the proposed control method. Three numerical simulation results confirm the effectiveness of the proposed method.