Research On Drive-response Shape Asymptotic Synchronization Control For Chaotic Systems And Its Application

The research of chaotic theory is an important branch of nonlinear dynamics,and the problem of chaotic synchronization is an important research direction of control theory.Due to wide application prospect in control science and secure communication,chaotic synchronization control has rapidly developed in recent years.At present,the kind of chaotic synchronization can be divided into complete synchronization,projective synchronization and lag synchronization and so on.It should be pointed that the above research in synchronization concentrated on the relation of state Euclidean distance between the drive system and response system,while the shape of their state trajectories are not involved and researched.Therefore,inspired by the above observation,the conception named as shape variables is proposed,and the drive-response shape asymptotic synchronization for chaotic systems and its application in secure communication have been investigated.The detail context is presented as follows:First,based on property of rigid body motion,the same shape between state trajectories is quantitatively described for 2 and 3 dimensional chaotic systems,respectively.Specifically,the description of same shape for 3 dimensional chaotic can be transferred as three 2dementional curves by means of coordinate plane projection.Then,with the definition of same shape of chaotic systems,the conception of drive-response shape asymptotic synchronization is proposed in this paper.Different from complete shape synchronization in existing literature,the proposed shape asymptotic synchronization avoid the use of arc length and curvature such that the limitation of system models can be handled,which expands the scope of application of shape synchronization and control methods for chaotic systems.Then,drive-response shape asymptotic synchronization controller for 2-dementional chaotic system is designed.The main method is that the problem of shape synchronization is transferred into the stability of tracking error system.By establishing the shape synchronization error between chaotic system and reasonable response system,an available controller for response system is designed to guarantee the error asymptotically converges to zero.According to Lyapunov stable theory,the effectiveness of proposed controller can be demonstrated,that is,the control objective of shape asymptotic synchronization can be achieved.And then,drive-response shape asymptotic synchronization controller for 3-dementional chaotic system is designed.By using projective systems of drive chaotic system and proposed response subsystems,the shape synchronization errors are established.Based on Linear Matrix Inequality(LMI)method and Lyapunov stable theory,a drive-response shape asymptotic synchronization controller for 3-dementional chaotic system is proposed.The effectiveness of proposed controller is proved mathematically and verified by numerical simulations.Finally,based on drive-response shape asymptotic synchronization control for 3-dimentional chaotic systems,a chaotic secure communication scheme is proposed in this paper.In this scheme,the original signal is covered up by the chaotic signals via the same shape between the state trajectories.In receiver side,by means of proposed response system with shape synchronization,the transmitting signal can be recovered.As the chaotic signal via the same shape trajectory of chaotic system can cover up the information of transmitting signal,the confidentiality of communication can be improved.Meanwhile,numerical simulations are established to verify the effectiveness of the scheme.