Chaotic Synchronization Between Two Rossler Systems Based On Differential Geometry Control Theory

The control and synchronization of Chaos systems have been the hotspots innonlinear science. With the development of chaotic synchronization，differentialgeometry method is widely used in nonlinear control theory, and becomes animportant branch of control theory. In this paper, the complete chaos synchronizationbetween two Rossler systems is investigated by the differential geometry method.In the first chapter, the types and the methods of chaos synchronization, the basictheorem, and the general steps of differential geometry method which applied tononlinear systems are introduced. In the second chapter, some literatures about newprogresses for chaos synchronization are introduced in detail, such as the use of thepassive control technique, non-periodic functions of feedback couplings method,drive-response synchronization method and the differential geometry method. Thethe generalized synchronization between Chua’s system and Lorenz system by usingdifferential geometry method is emphasized.In the third chapter, the complete synchronization based on the differentialgeometry control theory is investigated. Firstly, the necessary conditions for the errordynamical system is determined according to the Frobenius theorem, a real functionwhich makes relative degree of the original system equals to the space dimension ofthe system state is obtained. According to normal form of coordinate transformation,the error dynamic system is changed into Brunovsky standard form. Then, accordingto the quadratic performance index optimal control principle and Riccati matrixequation, the control law and the controller is determined. The Rossler system isselected as the example to illustrate the controller’s design process in detail.Numerical simulations are presented by Matlab to show the feasibility for thismethod.