Robust Controller Study For Chaos Control And Synchronization

Chaos control and synchronization study are international hotspots. In this dissertation, we did some deep and detailed studies on chaos control and synchronization. We put forward and discussed several new methods for chaos control and synchronization. The main contributions of this dissertation are as follows:(1) Chaos synchronization via linear controller was studied in detailed. At first, the chaos system was decomposed into two low dimension subsystems which were low dimension linear subsystem and low dimension nonlinear subsystem, respectively. Then, linear subsystem was synchronized via state feedback technology and nonlinear subsystem via linear controller by utilizing stability theory of cascade-connected system. Thus, the whole system was synchronized by linear controller. Synchronization on Liu system and Rossler system were given to illustrate the effectiveness of the proposed method, respectively. Meanwhile, simulations also show that the method has robust against small parameter perturbation.(2) Synchronization on uncertain chaotic system was studied. Firstly, we derived nonlinear controller for exponent synchronization on uncertain chaotic system by utilizing observer design technology. We modified the derived controller which can synchronize chaotic system with any given accuracy for practical. But the derived controllers were assumed that both the norm of uncertainty and Lipschitz constant were known. However, conservative estimation on either the bound of uncertainty norm or Lipschitz constant would result in failure in deriving controller or controller realization for large feedback gain. In order to overcome the deficiency, we developed another novel controller via adaptive technology.(3) Arbitrary point stabilization for Lorenz system with external disturbance was analyzed and a novel variable structure controller was put forward. Compared with the existing variable structure controller, it can not only stabilize the state to the vicinity of the desired point with predict error, but also assume that at least one of state component will be droved to the corresponding component of the desired point. Two compared simulations were given to illustrate the effectiveness and validity of the provided method.(4) Stabilization problem for a kind of chaotic system with parameter perturbation was studied. Based on adaptive technique and Backstepping design method, we derived two different kind of controller (control input was added to different differential equation) for Lorenz system, Chen system and Lu system with time varying parameter perturbation. Compared with existing controller based on Backstepping design method, the derived controller has strong robust against time varying parameter perturbation. The method can also provide a paradigm or framework to design a robust controller by utilizing Backstepping design technique.(5)Chaos tracking problem on chaotic system with parameter perturbation, external perturbation and structure perturbation was studied. Nonlinear item on lots of well-known chaotic system such as Lorenz system, Chen system, Lu system and Rossler system is not satisfied with Lipschitz condition strictly, we described these uncertainties by a simple norm polynomial inequality. Based on the described inequality, a novel adaptive tracking controller was put forward by rigorous mathematical proof. Simulation shows the effectiveness of the proposed method.