The Study Of Chaos Control And Synchronization Based On Backstepping Sliding Mode Control Method

The theory of chaos control and synchronization have been widely used in many fields with its continuous improvement and development. Particularly, the methods of chaos synchronization and related theory are constantly enriched and developed in many specific applications. In recent years, the methods of sliding mode variable structure control and backstepping control particularly has been attracted much attention. After the basic concepts and methods are outlined, the recent developments about sliding mode control and backstepping control method will be introduced that concerned with chaos control and synchronization. By effective combaination of the two method mentioned, the problem of chaos control and chaotic system synchronization are discussed based on the Lyapunov stability theory. As a example, a class of uncertain chaotic systems are used to discuss the tracking problem for command signal and the corresponding controller is designed. The effectiveness and universality for the method are verified by the simulation with Arneodo system. Besides, the realization of the chaos synchronization with same methods is demonstrated with two Rucklidge chaotic systems, the controller designed by backstepping sliding mode and parameters adaptive rate are obtained. Finally, the validity of the control scheme is verified by simulation. It show that the chaos synchronization between two Rucklidge systems is achieved and the uncertain parameters in the response system has been identified. This method can be applied in chaos synchronization between different chaotic systems.