Research On The Chaotic Identify Synchronization Between Autonomic Chaotic Systems Based On State Feedback

Chaos is the quasi-stochastic phenomenon which is produced in a certain nonlinear system. It very fits for secure communication by reason of its characters of similar to noise. Chaotic synchronization is the key of secure communication so the realization of secure communication using chaotic synchronization is the mostly researched field of chaos and its applications in recent years. Chaotic synchronization is the theory basis of secure communication and is an important aspect as well through which people study chaotic principle. The study has great theoretical signification and value in application. At present, there are some general problems in the research of chaotic synchronization. Some synchronization methods are too difficult to achieve physical implementation, and usually excessively change the original non-linear structure of chaotic system, others are proposed to solve certain problems and don not possess universality. It is a problem in need of giving a method which is easy to achieve physical implementation and can be used widely based on little changing the original non-linear structure of chaotic system.Making point against the problems above, the chaotic synchronizations between some systems and between different systems are studied in this thesis based on the idea of state feedback in control theory while the systems are continuous and autonomic. Some simple approaches are given to different types of chaotic synchronization. Firstly, we can realize the identify synchronization between the same continual chaotic systems by linear feedback method. At the same time, an estimation of the linear feedback gain matrix is obtained according to the relationship between eigenvalue and trace in matrix theory. Then based on analyzing the characteristic of hyper chaotic system, we can realize the identify synchronization between continual hyper chaotic systems according to the idea of variable structure control theory. This method can improve the robustness of system and obtain a faster synchronization response rate, which can be proofed by the numerical simulation results to the Qi's four-dimensional hyper chaotic system. Finally, taking Lyapunov stability theory as a basis and combining matrix norm theory, we propose a synchronization method which mainly solve the identify synchronization between different continual chaotic system. Based on the definition of chaotic synchronization the method has the requirement that the control decay to zero with error makes the long synchronization can be accomplished in limited energy. Simulation results show that this method is simple and effective, which can be applied to arbitrary two different chaotic systems with the same dimension, and ensure the rapid convergence of error and nonoscillatory.