| A number of methods in the field of chaos control and synchronization have been proposed for various types of chaos synchronization in which the projective synchronization is of particular concern.Zero dynamics has been one of the focuses of attention,but there are a few applications in chaos synchronization based on differential geometry method that found in literature recently,and its effectiveness is found in our investigation.In this paper,the projective chaos synchronization is realized through the partial feedback linearization for the error system in which the controller of the zero dynamics is designed independently.In the first chapter,the basic theory of differential geometry is introduced briefly,including the lie derivative,the total relative order,the partial feedback linearization and the zero dynamics.In the second chapter,the typical literature about the projective synchronization in recent years is introduced.In the third chapter,after the zero dynamics is formed by proper selection of control inputs,the control scheme is proposed for projective synchronization between hyper-chaotic systems.Selections of the control inputs mentioned above make the total relative order of the error dynamics system less than the system dimension so that the non-minimum phase zero dynamics subsystem and the partial linearization subsystem are constructed by partial feedback linearization.Therefore a compound control scheme for the projective chaos synchronization is derived in which the control of the partial feedback linearization is combined with the controller designed independently in the zero-dynamics that makes it become convergent,the efficiency of the control scheme can be improved obviously.Finally,the numerical simulations are made to verify the effectiveness of the control strategy and the identical hyper-chaotic systems are taken as the examples such as the hyper-chaotic Liu systems,hyper-chaotic Rossler systems and hyper-chaotic Chen systems. |
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