Research On Synchronization And Application Of Continuous Chaotic Systems

In recent years, chaos are widely studied and applied in secure communication and other fields , because of its characters of sensitive to initial conditions, similar to noise and continuous, wide-band frequency spectrum. However, the theory of chaotic control and synchronization is still very unripe presently, and until now there are a lot of problems on theory and technology unsolved. Considering some problems existing in the studies of chaotic synchronization at present , the problems of chaotic synchronization on theory , approaches and application, etc are discussed in this paper, with the continuous chaotic systems as the objects. The main purpose is to provide theory approaches and expand theory foundation for chaotic synchronization.Firstly, considering the fact that chaotic synchronization is only defined from stability property with its capability ignored, a redefinition of chaotic synchronization was given from both convergence property and its capability in this paper. And this not only perfects the definition system of chaotic synchronization, but also lay an effective theoretical foundation for the studies of chaotic synchronization in the latter chapters.Secondly, considering most approaches of chaotic synchronization that put forward already are based on stability of nonlinear chaotic synchronous error system, the problems of chaotic synchronization based on linearization by feedback were discussed in this paper, using an idea of linearization by feedback of chaotic synchronous error system. On the premise that the states of the aim chaotic system can be measured, an approach based on linearization by feedback was proposed for identical synchronization (IS). Further, generalized synchronization (GS) approaches were presented, too. The approachesbased on linearization by feedback for chaotic synchronization can change the nonlinear chaotic synchronous error system into a linear system, as a result, the synchronous problem based on the complicated nonlinear system is transformed into a stability problem of the simple linear system, and so the convergence property and the capability of chaotic synchronization can be discussed by the asymptotic stability of chaotic synchronous error system. Theoretical analysis and simulation results had verified the validity of the approaches.Again, from the point of view of improving the capability of chaotic synchronization, a theorem of exponent stability was applied to chaotic synchronization for the studies on chaotic synchronization based on exponent stability of chaotic synchronous error system in this paper. On the premise that the states of the aim chaotic system can be measured, the approaches of nonlinear feedback based on exponent stability for chaotic synchronization were put forward according to Lipschitz condition and the bounded property respectively. Since all the states of the aim chaotic system can't be measured in the application of chaotic synchronization, an approach of state observer based on exponent stability for chaotic synchronization was presented on the basis of the bounded property. The approaches of chaotic synchronization based on exponent stability can realize the rapid convergence of chaotic synchronous error system according to the exponent rule. Therefore, the quality of chaotic synchronization is guaranteed when reaching the chaotic synchronization. The simulation results had verified the capability by the approaches based on exponent stability for chaotic synchronization is satisfying.Then, a sliding mode control approach based on high gain state observer was presented in this paper, in order to realize the chaotic synchronization between parameters mismatching systems, even different chaotic systems. It combined with the methods of normaldescription of nonlinear system, high gain state observer and sliding mode control, etc, expanded the difference of parameter mismatching or the systematic structure into a new state, and made full use of the information that can be measured to design high gain state observer to estimate all the states of system. In the end, a sliding mode control which can be realized in the physics was designed, and realized the chaotic synchronization between parameters mismatching systems, even different systems successfully, when all the information from the aim chaotic system can't be acquired. Moreover, the approach need information from the aim chaotic system as little as possible, which will be very benefit for the application in the secure communication and so on. From the point of view of the quality of chaotic synchronization, the approach can arrive at a nice chaotic synchronous capability. Theory analysis and simulation results had proved the feasibility of the approach.Finally, the synchronization approaches above were applied in secure communication by amplitude masking modulation. In view of the interference problem of noise in the transmission channel, the de-noising approach by wavelet transform and wavelet pocket was imported into the secure communication systems based on chaotic synchronization, which improves the capability of anti-noise greatly for the communication systems. In order to increase SNR further and realize a better result of de-noising, a de-noising approach based on floating-threshold wavelet pocket was introduced in the secure communication systems based on chaotic synchronization. The simulation results had showed the approach can suppress the interference of the channel noise effectively, and the effect of secure communication based on chaotic synchronization is satisfying.