Minimum Time Synchronization of Chaotic Systems via Numerical Optimal Control Techniques

Abstract

Chaos synchronization has attracted much attention in recent decades since it has not only brought theoretical challenges but also could be applied to many real-world applications, such as digital communication, complex networks, and semiconductor lasers communication systems. We consider the minimum time problem of chaos synchronization via optimal control computation. The general synchronization scheme consists of identical/non-identical drive and response chaotic systems. We propose a novel computational approach to compute the minimum synchronization time of the drive-response chaotic systems and the corresponding optimal controls in a finite time horizon. By the control parametrization technique, the minimum-time chaos synchronization problem is transformed to an optimal parameter selection problem in two stages. A computational synchronization algorithm is hence devised to compute the minimum synchronization time and the optimal controls. For illustration, an exemplary scheme of Lorenz–Rossler chaotic systems is given to demonstrate the effectiveness of the proposed algorithm.