Research Of The T-S Fuzzy Model’s Chaotic Control And Synchronization Control Of Fractional Order Chen System

Chaos phenomenon refers to a kind of nonlinear science motion which is determined but unpredictable,and it is a complex phenomenon that appears to be random and inherently random in a deterministic system.A deterministic system means that the chaotic system is described by certain dynamics equation.The randomness of chaotic itself has intrinsic randomness,and the system performances long time behavior unpredictability.Not only chaotic phenomenon exists in integer order equation,but also exists in fractional order differential equation.However,because of the complexity of the chaotic system itself and extremely sensitivity to initial value making the study of chaos control is more challenging and important practical significance.In this paper,based on the T-S fuzzy model,integer order chaotic systems and fractional order chaotic systems are studied,and the synchronization control of the fractional order Chen chaotic systems is studied at same time.The main content of this paper is researched as follows:Firstly,the control problems of the integer order chaotic systems are studied based on T-S fuzzy model.Based on T-S model design of a fuzzy controller to continuous integer order chaos system,based on the Lyapunov stability theorem gives proof to the stability of the system.Sufficient conditions for the stability of the system are obtained.In a Duffing chaotic system,using computer simulation in Matlab further verifies the system’s stability.Secondly,the fractional differential equation is combined with chaotic systems,and in this chapter the control problem of fractional order chaotic systems is researched based on T-S fuzzy model.A fuzzy controller is designed for fractional order chaotic system based on T-S fuzzy model,according to the definition of fractional differential and Lyapunov stability theorem,the stability of the system is proved.An important criterion for the stability of this system is obtained.Then in the fractional order Lorenz and Chen chaotic system,using computer simulation in Matlab further verifies the stability of this system.Finally,a new method is researched to design a nonlinear synchronization controller for fractional order Chen chaotic system.For this system based on the stability theorem gives proof to the stability of the system.Sufficient conditions for realizing system synchronization are obtained.By using Matlab computer simulation further verifies the stability of this system.