Researches On Chaos Suppression And Synchronization Via Impulsive Control Theory

Chaos control has been paid more and more attention in the current research because of the complex dynamic behaviors and the potential applications of chaos. Among the theory of chaos control, chaos suppression and synchronization are two important directions. On the other hand, due to its distinctive advantages, impulsive control has been applied in many fields successfully. Therefore, how to utilize the impulsive control theory to realize the suppression and synchronization of chaotic systems becomes a novel research subject. Based on the theory of Lyapunov stabil-ity, the theory of impulsive differential system, and linear matrix inequality (LMI) technique, we study the improved impulsive control approach to delayed chaotic systems, and the asymptotic synchronization, exponential synchronization and more practical synchronization with error bound for serval famous chaotic systems. The main contributions of this dissertation are as follows:1. To the impulsive control for a class of nonlinear systems with time-varying delays, an improved impulsive control scheme is proposed. Based on the Lyapunov-like stability theory, some new sufficient conditions are derived. Compared with the existing results, the derived criteria can be verified easily and some unnecessary restrictions are removed. The results provide a more universal framework for impulsive control of the nonlinear delayed systems, which provides an important theoretical foundation for applying impulsive control theory to the secure communication based on chaos synchronization.2. To the complete synchronization problem of a class of non-delayed chaotic systems, an effective impulsive control method is proposed. The method uses linear state error feedback as the control signal to realize the global asymptotic synchronization of two identical chaotic systems. Based on the theory of im-pulsive differential equations, some new global asymptotic synchronous criteria are proposed. The impulsive instance can be either the whole impulsive se-quence or the odd one. In particular, some simple and practical conditions are derived by equal impulsive instance and control gains. In addition, the relation between the impulsive distances and the system synchronization performances is discussed. Compared with the existing results, the derived conditions are less conservative and the stable region is enlarged. Furthermore, the impulsive control is simple, efficient and adequate for most famous chaotic systems.3. A practical stability-based impulsive control for synchronization of a class of unified chaotic systems with channel time-delay and parametric uncertainties is proposed. The practical stability of impulsive synchronization between two nonautonomous chaotic systems is studied, which is equivalent to that of the synchronization error system at the origin. Based on the theory of impulsive differential equations, the criterion for the practical stability of the synchro-nization error system at the origin is presented.4. A practical impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed, and the error dynamics can con-verge to a predetermined level (so-called synchronization with error bound). For the above robust synchronization problem, an effective impulsive con-trol scheme (so-called dual-stage impulsive control) is proposed. Some more rigorous and less conservative conditions are presented, which provides an im-portant theoretical foundation for the synchronization of multi-perturbation chaotic systems.5. The synchronization scheme between chaotic systems with impulsive and stochastic perturbations is studied and an improved Halanay inequality for stochastic differential equations is presented. The designed time-varying de-layed feedback controller can guarantee exponential synchronization of chaotic Lur’e systems with parametric uncertainties. Second, the global impulsive ex-ponential synchronization of stochastic perturbed chaotic delayed neural net-works is studied (impulsive signals serve as controller). Furthermore, by using a novel optimization control algorithm, the minimum problem with two non-linear terms coexisting in LMIs is solved effectively.6. By establishing an efficient impulsive delay differential inequality, some new sufficient conditions expressed in the form of LMIs are derived in order to real-ize the robust global exponential synchronization of uncertain chaotic delayed neural networks. Furthermore, the designed dual-stage impulsive controller can not only achieve the exponential synchronization with error bound, but also estimate the exponential synchronization rate.