Chaos Synchronization of Optical Systems via a Fractional-Order Sliding Mode Controller

Abstract

In this chapter, one investigates the chaos synchronization of a class of uncertain optical chaotic systems. More precisely, one also presents a systematic approach for designing a fractional-order (FO) sliding mode controller to achieve a rapid, robust, and perfect chaos synchronization. By this robust controller, it is rigorously proven that the associated synchronization error is Mittag-Leffler (or asymptotically) stable. In a numerical simulation framework, this synchronization scheme is tested on many chaotic optical systems taken from the open literature. The obtained results clearly show that the proposed chaos synchronization controller is not only strongly robust with respect to the unavoidable system's uncertainties (as unmodeled dynamics, and parameters' variation and uncertainty) and eventual dynamical external disturbances, but also can significantly reduce the chattering effect.