Nonlinear Chaotic Systems With Feedback And Non-feedback Control

Chaos control has attracted more and more attention in the current research fields. We mainly engaged in the research work of two directions in chaos control, namely the problem of chaos control and synchronization for a class of new chaotic system and the problem of controlling chaos for a class of nonlinear Lienard system. The concrete contents of the dissertation are as follows:Chapter one introduces briefly the history and the current developments of the chaos theory. Then one focuses on the investigation history and the current situations of chaos control and synchronization. At last, the elementary knowledge used in this dissertation and the main contents are given.Chapter two investigates the problem of controlling a class of new chaotic system. It is found that the equilibrium points of the system are all unstable by the stability analysis. The chaotic trajectories of the new system with known parameters can be effectively guided to any unstable equilibrium point or period solution by the linear state feedback method. The stabilization of the equilibrium point for the system with unknown parameters is implemented by the adaptive feedback method. Numerical simulation results show both of the method can control the chaotic motion to the desired target orbit quickly and exactly. Moreover the controller is simple and realizable easily.Chapter three studies the problem of chaos synchronization for the new chaotic system. First the strict theoretical analysis of the system with the same parameters but different initial values is presented. Then the chaos synchronization is achieved by the active control. Furthermore, an adaptive feedback method based on the system identification is put forward. Using the strategy, the chaos synchronization of the systems with unknown parameters and different initial values is realized. Numerical simulation results show that the response speed of the two methods is fast. In addition the controlled system is stable against the parameter perturbation.Chapter four investigates the problem of chaos control for the extended Lienard system by the analytic and numerical method. Combining the theory of the strange attractor, the criterions of inducing chaos and suppressing chaos are established basedon the Melnikov method. According to the criterions, chaos control is achieved using non-feedback method for two classes of representative nonlinear systems. For Duffing-Rayleigh oscillator, chaos is induced by adding a bounded noise and for Duffing-van der Pol oscillator, chaos is suppressed by adding a parametric excitation. Meanwhile, various numerical methods which are the tools in common use to validate chaotic motion have been used to verify the correctness of proposed criterions and the validity of adoptive control methods.Chapter five concludes the work and points out some aspects to be further studied on chaos control and synchronization of nonlinear dynamic system.