| The chaotic control and synchronization for a class of hyper-chaotic systems with zero dynamics can be solved by differential geometry method.The property for the hyper-chaotic system with zero dynamics is a one that the relative degree is less than the system’s dimension.In this paper,a class of hyper-chaotic dynamical system with this property is considered as the object of investigation in which the chaotic control and synchronization are discussed respectively.Firstly,the hyper-chaotic dynamical system equation can be rewritten as the affine nonlinear system.Then the nonlinear coordinate transformation is carried out in which the appropriate output function is selected and an improved condition for the coordinate transformation is applied,and the partial linearization chaotic system equation on a new coordinate system is obtained.Finally,the asymptotic stabilization controller or identical structure synchronization controller is derived through the control principle and the invertible transformation relation of the coordinate transformation under zero dynamics.In the first chapter,the nonlinear coordinate transformation and basis of the differential geometry method are briefed.In the second chapter,some typical examples for the chaos control and chaos synchronization based on differential geometry method are introduced.In the last chapter,the hyper-chaotic Lorenz system,hyper-chaotic Chen system and hyper-chaotic Rossler system are taken as examples and the control strategies both for chaos control and chaos synchronization are gotten.For the affine nonlinear system which is transformed from the hyper-chaotic dynamical system or error system,the relative degree is calculated based on the choice of an output function.In the end,chaos control or chaos synchronization controller can be derived through the nonlinear coordinate transformation under the condition that the Jacobian matrix is nonsingular.For case of the chaos control,the much different form of the controller can be given depends on the different choice of the output function.The effectiveness of the control strategies are proved by numerical simulation. |
