The Chaos Control And Synchronization Of Complex Dynamic System And Their Applications In Communication

At present, the complex dynamic system is widely used in communications, finance, biology and many other subjects. Complex chaotic system is a typical com-plex dynamic system. Since complex Lorenz equation has been proposed in1982, complex chaotic systems have played an important role in many fields of physics, es-pecially in communication. The complex variables increase the content of transmit-ted information and improve the safety. The control and synchronization of complex chaotic systems is becoming one of hot spots of chaos-communication. Therefore, this thesis focuses on the control and synchronization of complex chaotic system and its application in secure communication. The main work and innovation points are as follows,1. The control and synchronization of real chaotic systemFor continuous system, we propose cumulative error controller. The controller is the linear function of cumulative error in essence, which can be realized by RC circuit in practical engineering. For discrete system, we put forward error feedback dynamic matrix. It is similar to the state feedback matrix for linear systems; but the former is time-varying and converges to a constant matrix. The controller includes coupling information of state variables, and updates online according to the gradi-ent descent method. Using the coupling relationship between variables, we present whole matrix control and partial matrix control. For partial matrix control, all vari-ables can reach the expected value only by the control of some variables, which is easy to implement in practice. However, the above controllers only can realize the stabilization of the fixed point and self-synchronization. Therefore, we combine with the speed gradient method and the nonlinear function control, and realize the smooth tracking of arbitrary bounded reference signal and parameter identification for continuous chaotic systems with unknown parameters. 2. The modified projective synchronization with complex scaling factor and parameter identificationWe propose modified projective synchronization with complex scaling factors (CMPS). Since complete synchronization (CS), anti-synchronization (AS), projec-tive synchronization (PS) and modified projective synchronization (MPS) are special cases of CMPS, CMPS contains existing works and extend previous works. Consid-ering all possible cases of unknown parameters and bounded disturbance, we design CMPS controller which contains convergence factor and dynamical control strength, and then we draw on the sufficient condition and necessary condition that the un-known parameters converge to their true values based on the persistency of excitation and linear independence. We also discuss the method to change the scaling factors to identify the true values of the parameters, which is important in the practical control system. In addition, CMPS establishes a link between real chaos and complex chaos. Therefore, based on speed-gradient method, we first design adaptive CMPS schemes including pseudogradient condition.3. Complex function projective synchronization of complex chaotic system and its application in communicationWe present complex function projective synchronization (CFPS). CS, AS, PS, MPS, full states hybrid projective synchronization (FSHPS), function projective syn-chronization (FPS), modified function projective synchronization (MFPS), general-ized function projective synchronization (GFPS) and CMPS are the special cases of CFPS. Therefore, CFPS, which has rarely been explored, will contain most existing works and extend previous works. For complex system with unknown parameters, we report CFPS schemes. Aiming at coupled complex chaotic systems, we design a novel communication scheme based on CFPS. The essence of this scheme is chaotic masking, but the transmitted signal is the derivative of the product of the information signal (used as complex scaling function) and chaotic signal. As the complex scal-ing functions are arbitrary and more unpredictable than real scaling functions, the possibility that an interceptor extracts the information from the transmitted signal is greatly reduced.4. Difference function projective synchronization of complex chaotic system and its application in communicationWe put forward difference function projection synchronization (DFPS) from the view of the difference of two functions. CS and phase synchronization are its special cases. We design DFPS controller, and apply it to the coupling complex chaotic system, and design the communication scheme based on DFPS. This com-munication scheme is still chaos masking in essence, but the transmitted signal is the derivative of the sum of information signal and chaotic signal. It avoids the error which is produced when the state of drive system (as the divisor) is close to zero in the communication scheme based on CFPS.5. Self-time-delay synchronization of complex chaotic system arid its applica-tion in communicationWe put forward self-time-delay synchronization (STDS) of complex chaotic systems. STDS is an extension of self-synchronization, which further broadens the horizons of synchronization issues, and avoids several problems caused by time-delay. Time-delay complex chaotic systems can generate time series with high ran-domness and unpredictability which can improve the security in chaos-communication. Therefore, we study the characteristics of time-delay complex Lorenz system, and design a feedback controller to realize STDS. For coupling time-delay complex chaotic systems, we discuss the communication scheme based on STDS. This com-munication scheme refers to the time-delay produced in the transmission process, which is more close to the real situation. The adoption of time-delay complex chaotic systems further enhances the effect of secrecy.To sum up, we study chaos control and synchronization of complex dynamical system and its applications in communication, and present the definitions such as modified projective synchronization with complex scaling factors, complex function projective synchronization, difference function projective synchronization and self-time-delay synchronization. We introduce the complex variables into the chaos- communication, which promote the development of the complex dynamic system, and provide the theoretical basis for strengthening security of communications.