Anti-synchronization For Hyper-chaotic Systems Based On The Differential Geometry Method And Zero Dynamics

The application of the partial feedback linearization method in the field of the chaos control and synchronization has received more and more attention based on the differential geometry theory,but there are a few literatures in the investigation for the chaos control and chaos synchronization in which the zero dynamics characteristics is applied.In this paper,the anti-synchronization between identical structure hyper-chaotic systems is achieved based on the differential geometry theory,and a control scheme is proposed with the application of the zero dynamics characteristic.In the first chapter,the basic knowledge of the differential geometry method are briefed,including the relative order and total relative order of vectors.Then the method of the local coordinate transformation,standard form and zero dynamics output are introduced in detail.The second chapter,some typical examples are shown to reflect the anti-synchronization control of chaotic systems in recent years,and the necessary and sufficient condition for the anti-synchronization between the chaos systems is summarized.In the third chapter,the anti-synchronization between hyper-chaotic systems is realized based on the differential method and zero dynamics,in which the hyper-chaotic Lorenz system,hyper-chaotic Chen system and hyper-chaotic Rossler system are taken as examples respectively.After the total relative order of the system is extended by a linear coupling in the affine error dynamics system,two subsystems obtained through partial feedback linearization,and control of the zero dynamics is designed independently to ensure the convergent.Finally,the hybrid control scheme is derived by the combination of the optimal control principle of the quadratic performance index.The Simulation shows the effectiveness of the control scheme.