Study On Optimal Control For Chaotic System Based On T-s Fuzzy Model

The study of chaotic control not only is a high degree of theoretical value, but also has far-reaching practical significance. Since it is found that the chaotic systems can be controlled, the control of chaotic systems is attracting great attention, many methods of chaotic control are constantly proposed. Based on the theory,in this paper, the problems of the stabilization control of chaotic systems and the tracking control of chaotic systems are studied. The details are clarified as follows:Firstly, the stabilization control of the continuous chaotic system is studied, because of the nonlinear characteristics of chaotic systems, it is hard to directly use optimal control theory for the continuous chaos control, at first, to solve this problem, TS fuzzy model is used for chaotic system modeling in this paper, thus, optimal controller can be designed for local linear subsystems, and the chaotic system is controlled. The effective of the control method is confirmed by the simulation experiments of the Chen system and hyperchaotic Lorenz system.Secondly, the stabilization control of the discrete chaotic system is studied; And similar to continuous chaotic system, it is also difficult to directly using optimal control theory for controlling discrete chaos, in this paper, first of all, the discrete chaotic system is modeled based on TS fuzzy model, then, the optimal controller of every linear discrete subsystem is designed on the optimal control theory of discrete systems, thus the controller of the discrete chaotic system is designed, simulation experiments of the generalized Hénon system and Hénon system show the effectiveness of the method.Finally, the tracking control problem of chaotic systems is studied, in order to let a controlled system track the expected chaotic system, firstly, the two chaotic systems are modeled based on TS fuzzy model, then, according to the connection among the subsystems, the two chaotic systems are connected by the augmented vector and augmented matrix, thus, the optimal output controller of each system is designed on optimal control theory, simulation experiments of chaotic systems of the same structure with different initial states and chaotic systems of different structures with different initial states of with different initial states verify the effective of the method.