Complete Synchronization Of High Dimensional Chaotic Systems By Combining Differential Geometry With Coupled Synchronization Method

In recent years,the control theory of nonlinear system based on the differential geometry method has become a hot spot in the field of chaos synchronization control.In this paper,a complete synchronization between high-dimensional chaotic systems is realized by combining the differential geometry method with the bidirectional linear coupling.The error dynamics system is divided into linear subsystem and zero dynamic subsystem by adjusting the relative degree of nonlinear system and the process of partial feedback linearization.The linear subsystem is converged by imposing an outer loop controller,while the zero dynamic subsystem is kept stable by applying an additional designed controller.The zero dynamic subsystem is an internal process which is uncontrollable normally by an outside designed controller,but it can be overcome in our scheme and the bidirectional linear coupling is introduced to accelerate the convergence efficiency and stability of zero dynamic problems.In Chapter 1,the related basic theory of differential geometry is introduced,including Lie algebra of vector field and vector field,partial state feedback linearization of MIMO system,and bidirectional coupling method in chaos synchronization control.In Chapter 2,three typical documents are taken as examples to show the important progress about the differential geometry method and coupling control synchronization method in the field of chaos synchronization control,the nonlinear control method of multi-input multi-output nonlinear non-minimum phase system,new results for exponential synchronization of linearly coupled ordinary differential systems and bidirectionally coupled synchronization of the generalized Lorenz system.In Chapter 3,a five-dimensional chaotic system is chosen as an example and a synchronization scheme is proposed by the combination of bidirectional coupling control and outer loop control.After the bidirectional coupling controller and a controller for adjusting the relative degree of the system are simultaneously introduced,the error dynamic system is transformed into a linear subsystem and a zero dynamic subsystem by nonlinear coordinate transformation.The bidirectional coupling controller in the zero dynamic subsystem is designed independently in which the coupling coefficient in the matrix condition is determined.In Chapter 4,it is another example that is more complex than the above one by the same method to shows that it can be used as a normal method for the chaos synchronization control of high-dimensional chaotic systems,and the only different point is the appropriate adjustment for the relative degree of the system in different case.Finally,the numerical simulation is carried out for the above two examples respectively to verify the effectiveness of the proposed scheme.