Output Tracking Control Of The Four-dimensional Hyper-chaotic Systems Based On Differential Geometry Technique

The output tracking control for the nonlinear system has been the one of the hot spots in the field of the chaos control in recent years,and the differential geometry method is distinctive among these control strategies,especially the state feedback linearization method.In this paper,a control scheme of the output tracking control for four dimensional hyper-chaotic system is investigated by the differential geometry method in detail.Firstly,a brief introduction about basis of the differential geometry method which will be applied in the control for nonlinear system is given,including the vector field,the Lie derivative,the relative degree,the nonlinear coordinate transformation and the state feedback linearization for the nonlinear system.Then,some typical methods which is used in that field in recent years are introduced such as the optimal tracking control based on the approximation-error-ADP method,adaptive fuzzy tracking control using disturbance observer and the tracking control based on linear matrix inequalities.In the third chapter,the control principle that aimed at the tracking control law is described in which the nonlinear system is turned into a canonical form by the nonlinear coordinate transformation and the feedback linearization is carried out.As an example,the output tracking control strategy is derived for the four-dimensional Rossler hyper-chaotic system in case of ?(28)3 and ?(28)2.Another example is for the Lorenz hyper-chaotic system in case of ?(28)2 and ?(28)1.Finally,the numerical simulation is carried out for the two examples to make the output signal tracking several reference signals and the effectiveness of the proposed tracking control strategies are proved.