Synchronization in the Genesio-Tesi and Coullet system using a fractional-order adaptive controller

In this paper, an adaptive fractional-order controller has been designed for synchronization in a pair of topologically inequivalent systems, the Genesio-Tesi and Coullet 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. The stability of the closed-loop PID control system is also guaranteed. The simulation results indicate the significance of the proposed controller as a control signal.