Synchronization of Chaotic Fractional-Order Genesio Tesi -Coullet Systems via Fractional-Order Adaptive Controller

This paper presents a fractional-order adaptive controller based on sliding mode control for synchronization of commensurate fractional-order chaotic systems. The adaptive controller is a fractional PID controller, which the coefficients will be tuned according to a proper adaptation mechanism. Fractional PID coefficients are updated using the gradient method when a proper sliding surface is chosen. To illustrate the effectiveness and performance of the controller, the proposed controller is implemented on chaotic fractional-order Genesio Tessi and Coullet systems. Performance of fractional-order PID adaptive controller (PαIλDμ) based on synchronization error, and control signal is compared with the conventional adaptive controller (PID) and sliding mode controller (SMC). The simulation results show the efficiency of the proposed controller.