Lag Synchronization Of High-dimensional MIMO Affine Chaotic Systems Based On Sliding Mode And Zero Dynamics

In the field of chaos control and synchronization,the chaos synchronization of high-dimensional chaotic systems has become the hotspot.Due to the nonlinear complexity in the high-dimensional systems,it is difficult to improve the control more efficiently so that it has to be combined with other approaches.In this paper,a scheme for the lag synchronization between identical high-dimensional chaotic systems combined with the sliding mode control and the zero dynamics method is proposed.In the first chapter,the basic theory of differential geometry and sliding mode control in the zero dynamics subsystem are introduced summarily.In the second chapter,the three typical papers are introduced to show the recent progress about related study,including the optimal controller design for uncertain chaotic systems based on quadratic performance index,adaptive terminal sliding mode synchronization for uncertain fractional-order chaotic systems with disturbance and comparative analysis of optimized output regulation of a SISO nonlinear system using different sliding manifolds.In the third chapter,a lag synchronization scheme is proposed for a new five-dimensional chaotic system combined with the sliding mode control and the zero dynamics method.Firstly,the error dynamics system is transformed into the affine MIMO nonlinear system,an appropriate output function is selected so that the total relative degree of the system is less than the dimension of the system.Then,the error dynamics system is divided into linear subsystem and zero dynamics subsystem based on the differential geometry method in which the controller of zero dynamics subsystem can be designed by the sliding mode control method independently.In the last chapter,the further efforts are made to simplify the complexity and improve the efficiency for the control process in which the different output functions are selected and the boundness of chaotic system is taken into account.It is proved more flexible in the synchronization control for the higher-dimensional chaotic systems.The effectiveness of these control schemes are verified by the numerical simulations.