Study On Chaotic System Control And Anti-Synchronization Methods

Chaos theory is one of the most important nonlinear science which is viewed as the third revolution after the principle of relativity and quantum mechanics. The chaotic phenomenons exist in almost every discipline, such as mathematics, physics, chemistry, biology, medicine, philosophy, economy, sociology and so forth. Recently, the control and synchronization theory of chaos system has already gotten great improvements whilst the anti-synchronization theory is becoming more and more remarkable. It is believed that this research has a great future for practical usage.The value of this research is stated at the beginning of this paper. The summary of the domestic and foreign research is given also in this chapter. Then it gives the basic control theory which will be used for controller design of the anti-synchronization.In the next chapter, the realization of anti-synchronization for two bidirectional coupled chaotic systems is done by utilizing adaptive control method. The adaptive controller and coupled parameters are calculated based on Lyapunov control theory and minimum value theorem. It can realize the anti-synchronization by neither getting the exact range of the coupled parameters, nor getting the maximum value of the chaos system previously.Then, for a type of chaos system in which we do not have any idea of parameters, we use adaptive variable-structure control to realize the anti-synchronization of linearly bidirectional coupled chaotic systems. It is not necessary to know the maximum value of the system parameters which is done by the adaptive control law. The stabilization of this system is analyzed by using Lyapunov theory. The results of simulation prove that it has a faster speed to get anti-synchronization, and robust character is very good.Additionally, for a type of Hyperchaotic system with variable parameters, we use variable adaptive control which combines with both differential and integration. The aim of the integration control is to eliminate the limit that we must know the all differentials of the controllable chaos system. The adaptive law of system parameters is derived based on Lyapunov theory, which makes the system much more strong against disturbance. The differential control is used for weakening the chattering during the system tuning process.