Synchronization Control Of Nonlinear Systems

Chaotic systems are well known for their very complex nonlinear systems, and they have been received increasing attention in various disciplines, such as, climatology, biology, physics, automation and so on. The fundamental characteristic of chaotic systems are its sensitive dependence on initial conditions, that is, a small shift in the initial states can lead to extraordinary perturbation in the system states.Based on the Lyapunov stability theorem, this thesis studies the synchronization control of chaotic systems. The main contributions are listed as follows:(1) In chapter 2, an adaptive synchronization problem is investigated for a class of uncertain chaotic systems.By using the radial basis function networks, the unknown function of the master system is approximated, an adaptive neural synchronization scheme is proposed with the combination of backstepping technique and dynamic surface control. This proposed method, similar to backstepping but with an important addition, can overcome the "explosion of complexity" of the traditional backstepping by introducing a first-order filtering.(2) Chapter 3 presents an adaptive terminal sliding mode control method for anti-synchronization of uncertain chaotic systems.In this chapter, by fusion of the terminal sliding mode control and the adaptive control techniques, a robust controller is designed so that the states tracking error can reach the terminal sliding mode surface and converges to zero in a finite time.(3) Chapter 4 investigates the terminal sliding mode control method for anti-synchronization of chaotic systems containing dead-zone nonlinearity.In this chapter, based on the Lyapunov stability theorem, a terminal sliding mode controller is designed so that the states tracking error can reach the terminal sliding mode surface and converges to zero in a finite time. Finally, a Duffing-Holmes chaotic system is used to demonstrate the effectiveness and the feasibility of the proposed anti-synchronization scheme.