Adaptive Control Of Chaotic System With Uncertaiin Parameters

In this paper, the dynamic analysis and controlling of chaotic system are studied. The main content is depicted as follows:In the first part, the author analyzes systemically the history and international actualities of the research on chaos, and formulate the starting, developing and the future of this field.Secondly, the definition and the characteristic of chaos are presented. Then we formulate the theory of chaotic control which will be used in this paper, such as Lyapunov stability theory, Lyapunov exponent and Lyapunov function.Thirdly, a new chaotic system and its chaotic attractor are proposed. And the dynamic analysis of the system is following.Then, this paper investigates the method for controlling the uncertain Liu chaotic system with known parameters k and h via adaptive backstepping control. With the method, parameters identification and control can be achieved simultaneously and quickly with only one controller within finite steps. Numerical stimulations are provided to show the effectiveness and feasibility of this method.Finally, an improved adaptive backstepping design is proposed to control the uncertain unified chaotic system. At first, we prove that an improved adaptive backstepping design method with only one controller is unavailable. Then, we proposed another new backstepping design. With the improved method, parameters identification and control of the unified chaotic system can be achieved simultaneously with only one controller within finite steps. At last, numerical stimulations are provided to demonstrate the effect of the control and parameters identification with the improved method when the parameter is changing.