Synchronization of Chaotic Fractional-order Systems via Fractional-Order Adaptive Controller

In this paper, an adaptive fractional-order controller has been designed for synchronization of chaotic fractional-order systems. This controller is a fractional PID controller, which the coefficients will be tuned according to a proper adaptation mechanism. 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 implements on a pair of topologically inequivalent chaotic fractional-order systems. The Genesio-Tessi and Coullet systems. Performance of fractional-order adaptive PID controller ((PID mu)-I-alpha-D-lambda) on the basis of speed of synchronization, error of synchronization, and level of control signal, is compared with the conventional ones (adaptive PD controller) and sliding mod controller (SMC). The simulation results reducing the level of control signal indicate the significance of the proposed controller.