Projection Synchronization For High-dimensional MIMO Affine Chaotic Systems Based On The Differential Geometry Method

Some types of chaos synchronization such as full synchronization and anti-synchronization,etc.can be regarded as the extensions of projection synchronization,so projection synchronization is the important type of chaos synchronization.In recent years,the differential geometry method has attracted more and more attention,especially in case of MIMO in which it can be applied more flexibly,even though it showed its limitation in the case of SISO.In this paper,the projection synchronization problem between high-dimensional chaotic systems is studied with the differential geometry method combined with the zero dynamics method,and the zero dynamics subsystem can be controlled independently.In the first chapter,the related theories of differential geometry are briefed,which contains vector field,Lie algebra,partial feedback linearization and zero dynamics.In the second chapter,the typical literatures on chaotic synchronization are introduced in recent years,including the study of projection synchronization of chaotic systems and the application of differential geometry plane curve theory in chaotic systems.In the third chapter,four high-dimensional chaotic systems are taken as the examples in which the derivation of the control scheme is illustrated,including the Lorenz-type five-dimensional hyper-chaotic system,a new type of five-dimensional entangled chaotic system and six-dimensional Duffing-Lü chaotic system.After the error dynamics system is transformed into the form of MIMO nonlinear systems,the appropriate output function is selected so that the total relative degree of the system is less than the dimension of the system,and the error dynamics system is divided into two subsystems based on the differential geometry method.In this method,the controller for the zero dynamics subsystem can be designed independently and it can be converged with the time in different ways so that the projection synchronization of high-dimensional chaotic system is achieved by the aid of the outer loop controller.Simulation result shows the effectiveness of the control schem.