Research On Several Issues Of Chaotic Synchronization

Recently, with the rapid development of chaos theory, chaos has become a hot topic in academic. In this paper, using the theoretical proof and numerical simulation method, the author has studied several problems of the chaos synchronization. The specific content of this article are as follows:The author applies a nonsingular and fast terminal sliding mode in a class of chaotic systems, then proves the stability of sliding mode with Lyapunov method and the existence of the sliding mode. Moreover, an adaptive sliding mode controller is designed to achieve robust synchronization of the systems with the uncertainty external disturbance. The effectiveness of the method has been verified by numerical simulation.The presence of dead-zone nonlinearities in control input may cause serious influence of system performance and decrease the system response. The author proposes a sliding mode controller with adaptive law, in spite of dead-zone nonlinearity in the control input, to synchronize a pair of uncertain drive-response chaotic systems when we have unknown bounded uncertainty in the model.The problem of lag synchronization for a class of fractional-order chaotic systems with unknown parameters is proposed Based on fractional stability theory, lag controller and update law of parameters are obtained. By this method, lag synchronization of fractional-order chaotic systems can be achieved simultaneously.The author investigates the problem of chaos synchronization of a new hyperchaotic system. Two kinds of synchronization schemes for the new hyperchaotic system with certain parameters are presented. Also an adaptive control and a parameter update rule for are given for the synchronization of hyperchaotic system with unknown parameters.