Research On The Method For The Anti-synchronous Control Of High-dimensional MIMO Chaotic Systems Based On The Zero Dynamics

In the field of chaos control and synchronization,the methods of differential geometry theory and the partial feedback linearization have gradually become the hot spots in research,and the zero dynamics control method has also attracted more and more attention.However,there are few result about the solution in the zero dynamics problem by the method of the differential geometry combined with the partial feedback linearization,especially for the case of MIMO,even though the research in the traditional way is perfect enough.In this paper,the anti-synchronization between high-dimensional chaotic systems is achieved in which the zero dynamics characteristic is applied based on the differential geometry method and the partial feedback linearization,and a control scheme is proposed.In the first chapter,the basic knowledge of differential geometry principle and the zero dynamics theory are summarized briefly,including the concepts such as the vector field,Lie derivative,the zero dynamics,and the zero output problem of the regular shape.In the second chapter,the latest progress in research for the anti-synchronization control is introduced.In the third chapter,four high-dimensional chaotic systems are taken as examples,in which the error dynamics is divided into two subsystems by the partial feedback linearization based on the differential geometry method.For the zero dynamics subsystem the controller is designed with the methods of the active control or the back-stepping respectively,and then the anti-synchronization between the two high-dimensional chaotic systems is realized combined with the outer loop control.The effectiveness is verified in simulation for the two schemes.