The Study Of Chaos Synchronization Based On Adaptive Sliding Mode Control

With the rapid development of modern science and technology and the universal application of computer technology, the research of Chaos has been widespread concern. Because of the instability of chaos and the unpredictability of a long time trends, control and use of the chaos has became the key section of the chaos research. Therefore, with the put forward of chaos control and chaos synchronization theory, the boom of domestic and international research on chaos control and synchronization was begin. Since chaos synchronization has broad application prospects, it is always a hot research subject of nonlinear science field. Chaos synchronization applied to secure communication is a hot issue of chaos application. The chaotic communication has high level of confidentiality and large amount of information, so it is a potential research topic. In recent years, chaos synchronization applied to secure communication has great development at home and abroad.Nowadays, researchers have proposed wide variety of synchronization control methods, but due to the different of the synchronization method and the controller, the difficulty of implementation is different. So design a simple and easily achieved controller is practical significance to the application of chaos synchronization in secure communication. Variable structure sliding mode control has developed for sixty years, has become a relatively independent branch of study, it has become a design method of automatic control system. This control method has simple algorithm, good robustness and high reliability, so it is very suitable for the research on chaos synchronization.This paper is based on an idea of select a simple controller to implement the chaos synchronization, according to the sliding mode variable structure control theory, analysis the synchronization, anti-synchronization and hybrid synchronization of chaotic systems based on a single adaptive sliding mode controller. There are four parts in this paper. Firstly it has systematically introduced the chaos theory, including an overview of basic research of chaos, chaos control, chaos synchronization, especially introduced the concept of chaos synchronization, several common methods and current situation of research. In the second part, I introduced the numerical simulation of chaos synchronization and the basic theory of variable structure sliding mode control. Based on this theory and use the case of Chen chaos system, the chaos synchronization basic theory of adaptive variable structure sliding mode control has been analysis, numerical simulations are used to prove the effectiveness of the proposed method. In the third part, I discussed the chaotic anti-synchronization based on adaptive variable structure sliding mode control, use the Arneodo system, Chua chaos system as the case, through the theoretical analysis and numerical simulation proof this method can be used for anti-synchronization of chaotic system. And the detailed proof of Arneodo system theory and the numerical simulation result of Arneodo system and Chua chaos system have been given in the paper. In the last part, I discussed the chaotic hybrid synchronization based on adaptive variable structure sliding mode control, use the unified chaotic system as a case, theoretically proof the chaotic system's hybrid synchronization based on the adaptive variable structure sliding mode control, and the numerical simulation results are given.According to the theory analysis and the numerical analysis, I proof the effectiveness of chaotic synchronization, anti-synchronization and hybrid synchronization based on adaptive variable structure sliding mode control. Further more, the controller is single and easy to select, it is build a good foundation for practical applications of the chaos synchronization. Lastly, this method has good applicability, it can be extended to most of the chaotic system, also can be used in different structure chaotic systems, hyperchaotic systems, fractional-order chaotic systems, etc, what's more, it is hopeful implement in the circuit simulation and actual circuit, and so it has very broad application prospects.