The Synchronization Control Theory In Chaos-based Secure Communication And It's Application

Communication technology plays an very important role in the modern human society. However, the problems of information security also raise with the development of the information technology. More and more attentions have been drawn to information security, especially the field of secure communication, cryptography and security problem of network. Last century has witnessed the huge growth of the research of nonlinear science. Many theories and technologies, especially the synchronization control theory, have been adopted while investigating the problems of information security. The synchronization control of chaotic systems and complex network has become a hot researching field last decade. Among different control methods, impulsive control has drew special attention due to the advantage such as robustness against the disturbances, simple structure, less information redundancy and less bandwidth required in the transmitted signal. Therefore, in this thesis, we discussed the robust impulsive control of some nonlinear systems, including chaotic systems and complex network and some criteria of asymptotic stability synchronization, robust synchronization is obtained. Based on these criteria, a time-varying impulsive control scheme is designed. Moreover, a chaos-based stream cipher system is designed and the properties of this cryptosystem is analyzed.While implemented in real world application, it is difficult to achieve synchronization for analog chaotic systems. Thus it is highly desired to design a synchronization control scheme for chaotic system. In this thesis, a hybrid impulsive control scheme is proposed. Different of existing schemes, the impulsive signals are generated by local digital chaotic systems. The analog chaotic systems achieve asymptotic synchronization without transmitted signal in public channels. The synchronization and desynchronizaion between the analog system and digital system is also discussed. While discussing the synchronization of chaotic system, the parameters of chaotic systems are always required to known exactly and time invariant. However, these conditions are impractical as chaotic systems are inevitably exposed to an environment which may cause their parameters varying within a small range. Thus in this thesis, the robustness of impulsive control is discussed. A new method for analyzing the robustness and stability of impulsive synchronization with parametric uncertainties and mismatch is introduced. By analyzing the oscillation process of the error between two chaotic systems, we establish a quantitive relationship between the prescribed synchronization threshold, the length of impulse interval, the bounds of uncertainties and mismatch and the impulse intensity. The relationship provides a theoretical basis and a firm assurance for impulsive synchronization schemes including all the existing ones to be practically applicable such as the development of secure communication strategies now.In this thesis, the robust impulsive synchronization control is discussed using a new type of impulsive control with time-varying impulse intervals. The relationship between the length of fixed impulsive intervals and a prespecified bound is established by extending Gronwall's inequality. Based on this new result, a time varying impulsive control is proposed with the impulsive intervals that are adaptive to the states of the driving system. Compared with the existing results, the length of impulsive intervals is significantly enlarged in our scheme.Based on the theoretical results proposed before, a hybrid chaos-based stream cipher system is designed. The analog chaotic systems are driven by local digital chaotic system. Thus the analog chaotic systems can achieve synchronization without driving signals transmitting in public channels. Moreover, the digital chaotic systems are disturbed by local analog chaotic systems. It is proved that disturbed by analog chaotic systems, the digital chaotic system is nonperiodic. Thus, the degeneration process of the digital chaotic systems are prevented. The driving sequence generated by the digital chaotic systems are transformed by a nonlinear transforming algorithm. The key sequences are tested and proved to be with excellent properties of randomness and complexity.The robustness of impulsive control of uncertain complex network is discussed in this thesis. The complex network contains not only non-delayed coupling but also delayed coupling. Moreover, the uncertainties of the nodes are also considered. By extending the idea of time-very impulsive control, a robust impulsive control scheme for uncertain complex network is designed and some criteria. Based on this new result, a time varying impulsive control is proposed with the impulsive intervals that are adaptive to the states of the driving system. As such, the requirement of bandwidth for impulsive signal transmitting is reduced.