Synchronization Control Of Chaotic Systems

Chaos control has become one of the hottest issues in the current control field because of the complex dynamical properties and a bright future in application of chaos. Synchro-nization control of chaotic systems is one of the urgent problems for the theory of chaos control. The dissertation has discussed the theoretical research and applied research about the chaotic systems, the variety and control of synchronization, which can lay a solid the-oretical foundation and construct a practical method in secure communication. Based on the theory of Lyapunov stability, fault tolerant observer synchronization, hybrid projective complete dislocated synchronization, transmission projective synchronization, combination-combination synchronization and compound synchronization have been discussed. The main contributions of this dissertation are given as follows:The disturbances, parameters and faults were not considered for the previous observers synchronization of differential inclusion chaotic systems. The problem of fault tolerant full-order and reduced-order observers synchronization has been discussed for the differential inclusion chaotic systems with unknown disturbances, parameters and faults. Even if there are unknown disturbances and parameters in the drive system, a robust fault tolerant adaptive full-order observer can be used to realize chaos synchronization with the response system for some assumptions no matter if fault occurs or not. What’s more, a reduced-order observer differential inclusion response system which can synchronize part states of drive system is developed for the same assumptions. The fault-tolerant reduced-order observer is not affected by the unknown disturbances and parameters by choosing a special gain matrix and this makes it much more robust. For this reason, we can conclude that fault-tolerant chaotic synchronization based on a reduced-order observer is better than that based on a full-order observer to some extent. The influence of disturbances, parameters and faults can be fully recognized to provide theoretical basis for further application in the paper.The projective synchronization was realized for the corresponding state variables of chaotic system in the previous studies. A new scheme of general hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parameters identification is proposed under the framework of drive-response systems. By choosing a proper control input and the update rules, we realize the general hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parame-ter identification between two different chaotic systems and two identical chaotic systems. Complete synchronization, hybrid dislocated synchronization, projective synchronization, non-dcrivativc and derivative coupling and parameters identification arc included as its spe-cial items. In a way, it is being more flexible in choosing the hybrid factor to make commu-nications more reliable.Most of researchers mainly focused on the previous drive-response synchronization schemes within one driven system and one response system model, did not consider three or more chaotic systems. We mainly investigate the transmission projective synchronization of multi systems with non-delayed and delayed coupling via impulsive control. Based on the stability analysis of impulsive differential equation, the control laws and updating laws are designed to realize the transmission projective synchronization. Based on the advantages of projective synchronization and impulsive control, the transmission projective synchroniza-tion is realized by the impulsive control to enhance secure communication security. In our model, the synchronization among multi systems can be achieved through the other systems to overcome the trouble without affecting their synchronization and performance.The combination synchronization scheme for combination of two drive systems and one response system, which was realized in the previous model, is extended to the synchro-nization between a combination of two drive systems and a combination of two response systems. The novel combination-combination synchronization is realized by the nonsin-gular terminal sliding mode control technique for combination of two chaotic systems as drive system and combination of two chaotic systems as response system with unknown parameters in a finite time. On the basic of the adaptive laws and finite-time stability the-ory, an adaptive combination sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time for four different chaotic systems, the novel combination-combination synchronization will be realized in the finite time. The combina-tion system is more complex to enhance the security of communication. The combination of all the chaotic systems is regarded as the drive systems or response systems, such that we can design a universal combination of the drive systems, a universal combination of re-sponse systems, and a universal adaptive sliding mode controller for a nonsingular terminal sliding surface. According to our actual requirements, we chose the corresponding system or systems combination, the corresponding parameter values are given to the drive systems, and response systems to realize synchronization. We need not redesign the controller for two systems or systems combination every application. Too much time and energy are saved for our future practical application.For combination synchronization and combination-combination synchronization, chaotic synchronization are realized by simple addition and subtraction for the multi chaotic systems, however, we take into consideration not only addition and subtraction, but the mul-tiplication for the multi chaotic systems in our scheme. A novel kind of compound syn- chronization among four chaotic systems is investigated, where the drive systems have been conceptually divided into two categories:scaling drive systems and base drive systems. Firstly, a sufficient condition is obtained to ensure compound synchronization among four memristor chaotic oscillator systems based on the adaptive technique. Secondly, a secure communication scheme via adaptive compound synchronization of four memristor chaotic oscillator systems is presented. The unpredictability of scaling drive systems can addition-ally enhance the security of communication. The transmitted signals can be split into several parts loaded in the drive systems to improve the reliability of communication.This dissertation systematically discusses the synchronization problems of chaotic sys-tems and synchronization ways, and makes the further development of the theory of chaos and secure communication theory, which can provide theoretical direction for further secure communication research.