Control Of Chaotic Systems Based On Differential Geometry Method

Up to now, a variety of theoretical approaches for the chaos control and chaossynchronization have been developed. Most of these nonlinear controllers are designed basedon the Lyapunov’s stability theory，in which the methods of construction for each specialLyapunov function were depended on some skills that the designers used, and the appropriatecontroller can be obtained by the time differential of the Lyapunov function along thetrajectory of the error dynamical system. Recent years, the differential geometry methodapplied in the chaotic system control was gradually concerned that different from theLyapunov function method completely. In the thesis, some articles are introduced in detail inwhich the differential geometry method was adopt in some chaotic system.In the first two chapters of the paper, the fundamentals for the differential geometrymethod is introduced firstly, including the principles of Lie derivative, Leibniz rule and theprinciple of the linearization for nonlinear systems. Next, some new progresses in the studyused with the differential geometric method are introduced, such as the application inelectronic system friction, the elastic model and the charged particle control etc. In the thirdchapter, a control method is proposed for the chaotic system, and the controller for thepredetermined output state and its constraints are designed based on the differential geometricmethod. As an example, the Lorenz chaotic system and Rossler chaotic system are providedto illustrate the effectiveness of the obtained scheme to achieve the stable control，and toobtain a expected output. Simulation in Matlab shows the effectiveness and feasibility of theproposed methods.