The Research On Synchronization Approach Of Fractional-order Chaotic System With Time Delay Via Sliding Mode Control

The fractional order system with respect to the integer order system can better meet the practical and application of complex can have better performance in this area. Because of the existence of a large number of phenomena and the delay in nature, if only the fractional order chaotic system to describe the phenomenon is obviously not enough accurate,so now there are many domestic and foreign scholars in the control of fractional delay and synchronization of chaotic system and obtained some results, some corresponding control and synchronization methods have been developed. In these methods, the robustness of the powerful sliding mode control, when the system enters the sliding surface convergence set in motion can be fast and stable, so this method is used by many scholars. This paper firstly studies the synchronization of a class of fractional order chaotic systems, and then use the sliding mode control method is used to study the control and synchronization of fractional order chaotic control.The first chapter outlines the development degree of chaos. Then in the second section introduces three kinds of the definition of chaos, followed by the two definitions between Riemann-Liouvile and Caputo can be found Caputo the definition of derivative for initial condition initial conditions with the integer order differential equation is the same in form, so it has a physical situation is easy to understand and has more application in real life. The third section of this chapter introduces the need to use some lemmas and theorems on stability. Finally, in the fourth section introduces the method in numerical simulation of fractional order chaotic system and the fractional order chaotic system is needed.The second chapter mainly aims at the chaotic behavior of a new class of fractional order chaotic system bifurcation analysis to study the system, then presents the methods of control and synchronization, and to verify the feasibility of the proposed method by numerical simulation. The first section of the third chapter focuses on a class of fractional order chaotic systems with time delays by using the sliding mode control method, through the design of sliding mode controller is implemented to control the system, and get the stable condition of the system. Then the research on control and synchronization of the system, according to the research of the first section of this chapter, in section second, the synchronization controller is designed to realize the synchronization of the system and the numerical simulation to verify the feasibility of the proposed method.The first section of the fourth chapter focuses on a class of fractional order chaotic systems with time delays, in considering the randomness and disturbance due to system become more complex, so its control is very meaningful. This chapter mainly use the sliding mode control method to stabilize the system through the design of sliding mode corresponding controller and the stability condition of the system. According to the second part of this chapter, section second in a specific system design of the sliding mode controller to stabilize the system and through the numerical simulation to verify the feasibility of the proposed method.