The Research On Synchronization Control Of Fractional Order Chaotic System

The article mainly studied the chaotic synchronization methods of fractional-order chaotic systems. With the breakthrough development of fractional-order calculus theory in recent decades and the research of integer order chaotic systems synchronization method, fractional order chaotic systems synchronization has made breakthrough progress. Many scholars at home and abroad has done a lot of research work on fractional-order chaotic system synchronization, also got a lot of methods of synchronization. But compared to the integer-order chaotic systems, fractional-order chaotic system still has great space for development. In this paper, we choose the continuous-time chaotic systems as the objects, based on the theory of fractional-order chaotic system stability, combining theoretical proof and numerical simulation, verify the feasibility of fractional-order chaotic systems synchronization. All of works in the paper are as follows:1. This paper introduces the basic situation of chaos. The development process of chaos and the definition of chaos are introduced. And understand the main characteristic of chaotic systems, such as certainty, boundedness, ergodicity, the extreme sensitive dependence on initial condition, not long-term predictability, bifurcation, aperiodic, maximum Lyapunov index, etc. This paper briefly describes the definition of chaotic synchronization, the type of chaotic synchronization and several commonly used chaotic synchronization methods. Domestic and foreign research achievements and developing trend of fractional-order chaotic system synchronization are also made a simple introduction.2. An overview of the development history of fractional-order calculus. Introduce the definition of Riemann-Liouville fractional-order calculus, Caputo fractional-order calculus and Grunwald-Letnikov fractional-order calculus. And two kinds of solution method and four basic properties of fractional-order calculus are listed.3. In this paper, we propose an active sliding mode method combining active control theory and sliding mode theory to synchronize fractional-order chaotic systems. In the active sliding mode control strategy, fractional-order integrator is first introduced to obtain a novel sliding surface containing the all state components in the system and fractional order chaotic system is stable in the sliding surface. Then the gain matrix of the active sliding mode controller is obtained using the pole placement method. The existence and the stability of the proposed controller are analyzed based on Lyapunov stability theory and fractional stability theory. The simulation results of the fractional order Lorenz system, fractional order Lu system and fractional order Chen system verify the effectiveness of the proposed method.4. The TS fuzzy model will be used to model fractional order chaotic system. Parallel distributed compensation fuzzy controller is designed. Two sufficient condition for the robust stability of the fractional order error system are given. The sufficient conditions are formulated in the format of linear matrix inequalities. The problem of designing the fuzzy controller is converted into solving the linear matrix inequality. In addition, based on the stability theory of fractional order linear system, designed a state feedback controller, and realized two fractional order chaotic systems synchronization. Matlab numerical simulation of fractional order Rossler system and fractional order Lorenz system shows the feasibility and effectiveness of the method.