Neural Control for Synchronization of a Chaotic Chua-Chen System

Abstract

In this paper, the synchronization problem of a master-slave system composed by a Chua's oscillator as the master and a Chen's oscillator as the slave is considered. Although the states of both systems are available for measurement, a complete lack of knowledge about the parameters of the oscillators is assumed. In order to handle this high uncertainty condition, the proposed design is based on differential neural networks approach. A neural identifier approximates the unknown dynamics of Chen's oscillator by using a stable learning law. The exponential convergence of identification error to a bounded zone is guaranteed by means of a Lyapunov-like analysis. Based on the instantaneous mathematical model of Chen's oscillator provided by the neural identifier, a control law is developed in such a way that Chen's oscillator follows the dynamic behavior of Chua's oscillator. The tracking error converges to a bounded zone and all parameters of this neural controller are guaranteed to be bounded. A numeric example illustrates the feasibility of the proposed approach.