Synchronization Decoupling Control Of Chaotic System Based On The Differential Geometry Method

Currently,the synchronization disturbance decoupling of the chaotic systems has attracted a widespread concern in which the disturbances can be eliminated by designing decoupling controller to make the chaotic systems have same or opposite trajectories each other,including the synchronous decoupling,the mixed synchronous decoupling and the anti-synchronous decoupling.In this paper,the three types of synchronization between two chaotic systems will be dealt with by the differential geometry method.In the first chapter,the basic theories for the differential geometry method are introduced and the feasibility for which the chaotic system can be controlled with disturbance decoupling based on this method is proved.In the next chapter,some typical literatures’ research results to achieve decoupling control for nonlinear systems with same method are presented,such as decoupling control on the generators and car semi-active suspension,and the features of controller are illustrated in detail.In the third chapter,after the principle of the decoupling control is described,the Rossler system,the Lorenz system and the Coullet system are taken as examples respectively to derive the control strategy with the method of the decoupling control to achieve the three types of the synchronous decoupling between two chaotic systems.In the case of meeting the condition of decoupling,the error system is rewritten as an affine standard of the single-input single-output system and through a nonlinear coordinate transformation it is converted to a linear subsystem.Finally,the decoupling controller is derived based on the principle of the decoupling control.The effectiveness for the control strategy is proved by the numerical simulation.