Taming Single Input Chaotic Systems by Fractional Differentiator-Based Controller: Theoretical and Experimental Study

Abstract

A simple fractional differentiator-based controller is proposed to suppress chaos in a 3D single input chaotic system by stabilizing some of the fixed points. The tuning procedure for the proposed controller is based on the stability concepts in the incommensurate fractional order systems. To show the efficiency of the controller, some numerical simulations are given. Also, to evaluate the practical capability of the proposed controller, we experimentally apply it to control chaos in a chaotic circuit. Moreover, some mathematical analyses are presented to show the applicability of the proposed controller, when its structure is not exactly implementable.