Synchronization of Incommensurate Fractional-Order Chaotic Systems with Input Nonlinearities Using a Fuzzy Variable-Structure Control

This research work addresses the fuzzy adaptive controller design for a generalized projective synchronization (GPS) of incommensurate fractional-order chaotic systems with input nonlinearities. The considered master-slave systems are with different fractional-orders, uncertain models, unknown bounded disturbances and non-identical form. The suggested controller includes two main terms, namely, a fuzzy adaptive control and a fractional-order variable structure control. The fuzzy logic systems are exploited for approximating the system uncertainties. A Lyapunov approach is employed for determining the parameter adaptation laws and proving the stability of the closed-loop system. At last, simulation results are given to demonstrate the validity of the proposed GPS approach.