Research On Synchronization Of Continuous Chaotic Systems

For continous chaotic systems, synchronization between the same two systems and the different two systems is considered in this dissertation.Chaos synchronization is a hot topic in recent years, and it is broadly applied in practice, especially in secure communication. At present, many methods have been proposed for chaos synchronization, but most of them mainly care how to realize synchronization and do not care how to improve synchronous performance.For these reasons, this paper studies the synchronous problem between the same two chaotic systems and the different two chaotic systems by sliding mode control(SMC) and adaptive control. It achieves the following two goals:(1) Using adaptive control for chaos synchronization can improve synchronous applicability;(2) Using SMC for chaos synchronization can improve synchronous effect, because chaos synchronization is realized by the stability of sliding mode that is robust.The research results about the above regard are very few especially for chaotic systems with uncertainty and hyperchaotic systems. The study addresses the following topics:1. The concept of chaos and chaos synchronization is introuced, and the features and research status for chaos synchronization are summarized, and the problems for chaos synchronization are pointed. Furthermore, history and research results of SMC and adaptive control are overviewed, and their applications for chaos synchronization are introduced.2. The proposed methods for chaos synchronization focus on its realization, but its robustness is neglected. This paper overcomes the disadvantage by using SMC and improves the synchronous effect by designing suitable sliding manifolds and control laws.3. For certain chaotic systems, synchronization between the same two chaotic systems and the different two chaotic systems is discussed. In the study of these problems, it is important how to realize synchronization by designing suitable controllers that are simple, easily realizable and robust. The above goal can be achieved by using SMC. Some representative chaotic systems in theoretical research and practical applications are as examples in this paper, and the validity is proved from theoretical analysis and numerical simulations. Both single input and multiple input can be used in the design, thus the control mode is very flexible.4. To overcome with the uncertainty, we combine SMC with adaptive control and design adaptive sliding manifolds, and good effect is achieved by doing so in this paper. On the other hand, chaos synchronization is achieved by designing suitable parametric adaptive laws for chaotic systems with unknown parameters.5. Systematic motion may become worse, and synchronization may be destroyed with dead-zone nonlinear control input. Therefore, in order to avoid the situation, we take the synchronous problem for the unified chaotic system as an example and study the problem with dead-zone nonlinear control input. Finally, chaos synchronization is achieved by using SMC.6. Chaos synchronization for some hyperchaotic systems is studied by using SMC in this paper.7. The conclusions and the directions for the future research work are given in the end of the paper.