Command Filtered Adaptive Backstepping Fuzzy Synchronization Control of Uncertain Fractional Order Chaotic Systems with External Disturbance

In this paper, aim to synchronize uncertain fractional order chaotic systems with disturbances, a command filter adaptive fuzzy backstepping control method is proposed. A fractional order command filter is designed to solve the explosion of complexity problem in the backstepping framework. In particular, an error compensation signal is devised to reduce the filter error and improve the synchronization accuracy. Meanwhile, in the design of backstepping scheme, fuzzy logic systems are utilized to estimate unknown functions. Based on the Lyapunov stability criterion, the synchronization error can be ensured to ultimately converge to a small neighborhood near zero. Finally, a numerical simulation is given to verify the effectiveness and accuracy of the proposed scheme.