Chaos Synchronization Between Affine Hyper-chaotic Systems Based On The Zero Dynamics Method

The complete chaos synchronization between the identical hyper-chaotic systems is realized in the case of MIMO(multiple input and multiple output)hyper-chaotic systems based on differential geometry method in which the zero dynamics is constructed.There are a few literatures about similar research that is investigated by mean of the zero dynamics.In this paper,after the relative order of the system is adjusted appropriately,the two circumstances of the zero dynamics are considered that constructed from the error dynamics system,the non-minimum phase system and the minimum phase system,and the effective control scheme are proposed respectively.Firstly,the mathematics basis of differential geometry is summarized briefly,then the control principle for the zero dynamics of MIMO nonlinear system is introduced.In the second chapter,two typical related literatures are introduced in recent years.The first one is based on the classical control method for the nonlinear system and the second one is based on the differential geometry method.The two methods mentioned above are compared and analyzed to illustrate the characteristics of the differential geometry method.In the third chapter,the first circumstance is considered.The complete chaos synchronization between identical hyper-chaotic systems is realized based on differential geometry method in which the non-minimum phase zero dynamic subsystem is formed and controlled,and the hyper-chaotic Lü system,hyper-chaotic Lorenz system and hyper-chaotic Chen system are taken as examples respectively.After the total relative degree of the system is dynamically expanded and the output function is selected appropriately,the error dynamic system,which is transformed into an affine nonlinear system,is divided into two subsystems by the linearization of the partially state feedback.A hybrid controller is proposed that constructed by the controllers which are designed independently for the two subsystems above.In the final chapter,another circumstance is considered.The minimum phase zero dynamic subsystem is formed by the different selection for the output functions.The effectiveness of the control strategy is verified by the numerical simulations for the two circumstances.