Synchronization Between High-dimensional Chaotic Systems Based On The Independent Control In The Zero Dynamics

The synchronization between the identical high-dimensional hyper-chaotic systems is studied with differential geometry method.The synchronization of the high-dimensional hyper-chaotic systems is complicated,in which the chaos synchronization can be achieved only in the case in which the total relative degree equals the dimension of the system based on the differential geometry method,especially in the case of the MIMO nonlinear system.In this paper,the synchronization for the identical high-dimensional hyper-chaotic systems is realized by using the linearization of partially state feedback and the zero dynamic method.In the first chapter,some relative theory for the differential geometry is introduced briefly,including the description of the state space for the nonlinear system,the nonlinear transformation,the external linearization of the MIMO system in the case of the total relative degree less than the dimension of system and the zero dynamics problem.In the second chapter,the application of the zero dynamic problems and the synchronization of high-dimensional chaotic system based on the active control method are introduced through two papers.In the first one,the stability of strongly minimum-phase system is studied based on the zero dynamic method and dynamic feedback output.In the second one,the chaos synchronization of seven-dimensional hyper-chaotic system is studied with active control method.In the third chapter,the new five-dimensional hyper-chaotic system,the five-dimensional Chen hyper-chaotic system,the new six-dimensional hyper-chaotic system and the seven-dimensional heart-blood dynamic hyper-chaotic system are taken as the examples.For each of the four systems,after the system relative degree is changed with the appropriate output function,the systems is divided into two subsystems by the linearization of the partially state feedback,and the controller of the zero dynamic subsystem is designed by Lyapunov function method or active control method.Finally,the effectiveness of the control scheme is verified by numerical simulation.