Parameter Identification Of Chaotic Dynamical Systems And Its Application In Secure Communications

With the rapid development of information technology and the arrival of the era of big data, Internet technology and its application promote the economic development of country and improve the quality of life. However, while enjoying the convenience Internet brings, increasing number of data and information are suffering from various security threats, such as monitoring, steal and malicious tampering. The problem of information security has become the major problem that affects national security and social development of country in this day and age. The existing secure communication techniques are also facing increasing challenges. So the study about new secure communication methods is an important issue in order to ensure the secure communication in the research fields including communications, computer science and information technology.Due to inherent characteristics of chaotic systems, such as aperiodicity, noise-like, sensibility to the initial condition and the wide frequency chart, chaotic signal is highly unpredictable and has natural security that make it as a suitable carrier in secure communications. As the idea of chaotic secure communication was proposed in the early1990s, it has become a hot topic in the research fields of information security. The basic idea of chaotic secure communication is to transfer the message to chaotic signal in the transmitter, transmit the chaotic carrier in the public channel, and recover the message from the chaotic signal at the receiver. During the twenty years of development, domestic and foreign scientists and researchers have been working on chaotic secure communication models and related techniques from various perspectives, such as encryption algorithms, anti-attacking and chaotic devices. Under the influence of big data, future research directions of chaotic secure communications begin to move to digitization chaotic communications, multi-users chaotic communications, high performance chaotic communication, broadband wireless chaotic communication and so on.In general, there are some or all unknown parameters in chaotic systems of the chaotic secure communication model. Although systems under such uncertainties are hard to be controlled, such systems have high security when we modulate messages in the unknown parameters and therefore improve the security of chaotic communications. In order to control such chaotic systems, it is possible to use the adaptive parameter estimation method in nonlinear control theory which adaptively adjusts the controller to achieve the goal according to the state or the output. The main works of the dissertation could be summarized as follows:(1) A novel method is proposed to estimate unknown model parameters effectively by computing the rank of matrices. It also illustrates the special relationship between linearly independent condition and persistent excitation condition for the first time. Linearly independent condition and persistent excitation condition are two fundamental conditions in adaptive parameter estimation. But no one has explored the relation between them. Different from these two conditions, in some cases, the proposed Gram matrix method can reduce the computational complexity of linear independence and persistent excitation. So it is a more practical and efficient tool for parameter identification.(2) There are some drawbacks in some recent works on ignoring the conditions which ensure the parameter convergence. The definition of linear independence in parameter estimation did not pay attention to the restriction on the time domain. The correct definition of linear independence is given. In real-world applications, sometime the system satisfies the condition for a long time and sometime only satisfies for a finite time range. The long-time version and finite-time version of linearly independent condition, persistent excitation condition and Gram matrix condition are proposed. The impact of synchronization and persistent time of above three conditions on the results of parameter estimation are further analyzed. The case in the presence of noise is also considered and some measures to suppress the fluctuation caused by the noise are also given. All above methods can be easily applied in chaotic secure communications.(3) Based on the adaptive parameter identification methods, a chaotic communication model is designed by a multiple time-delay chaotic system to transmit multiple messages. The original messages are directly added to the system parameters and recovered at the receiver using the methods of adaptive parameter estimation. The total information carried in such chaotic communication model is larger than the value of any conventional chaotic communication scheme. Next, the idea of CDMA is applied in the above model. Based on the Walsh code, at the transmitter, multiple original messages are first modulated to Walsh code and then added to the parameters of chaotic systems. At the receiver, demodulate messages from the parameters by using inverse mapping of Walsh function. The total information carried in such chaotic communication model is larger than the value of above chaotic secure communication model. From the perspective of communication, such chaotic communication model improves the resource utilization. Our proposed scheme has potential application in the chaotic optical communications.(5) An idea to explore the influence of the transient process in synchronization phenomenon on the result of network topology identification is addressed. In the above, the chaotic communication consisted of single chaotic system was considered which realized the point-to-point chaotic communication. A number of chaotic secure communication systems compose a complex network. The adaptive parameter estimation methods are extended to identify the topology of complex networks. Some recent works showed that the topology identification would fail if the network is in a synchronous situation. As long as the proposed finite-time conditions are satisfied, we find that it is possible to estimate the precise connection topology during the transient process. After the successful identification achieved, it won’t change even if the synchronization is reached.