Synchronization Analysis And Control For Some Kinds Of Complex Dynamical Networks

Complex dynamical networks have been considered as an important approach for describing and understanding complex systems. From the point of view of study, all complex systems can be abstracted as complex networks which are represented by graphs in which individuals are denoted by nodes and interactions are denoted by links. In the past few years, much attentions on complex networks have been attracted by scholars. As a common phenomenon of the interacting units, synchro-nization is a representative topic in complex networks. Ubiquitous in various kinds of complex networks, synchronization is closely related to multiple realistic problems. Therefore, it is of great significance to investigate synchronization analysis and con-trol problem of complex networks. In this dissertation, by using Lyapunov stability theory, chaos synchronization theory, adaptive control theory, random control the-ory combined with linear matrix inequalities(LMIs) technique, the synchronization, robust stability and the corresponding control strategies are investigated for some kinds of directed(undirected) complex dynamical networks with multi-links, delayed complex dynamical networks and stochastic networked control systems. Main con-tents of this dissertation are as follows.(1) The idea of network split is presented according to the different transmission speed of the network links. Time delay is introduced to split the directed network with multi-links, and based on that a model of directed complex dynamical networks with multi-links is constructed, which is closed to the reality. The model offer the modeling basis to some networks in reality, such as transportation networks, communications networks, and so on. We take both directed and undirected network connections into account. Via the theory of Lyapunov stability combined with linear matrix inequalities technique, the method of decomposing the coefficient matrices of the delay items and the method of the free-weighting matrix, the delay-dependent synchronization stability criterion which is less conservative is derived in the form of linear matrix inequalities. When the interior coupling coefficients are linear, the linear and adaptive feedback synchronization controllers for the known and unknown exterior coupling coefficients are designed, respectively. When the interior coupling coefficients are nonlinear, the adaptive feedback synchronization controllers for the unknown exterior coupling coefficients are designed. (2) The problems of pinning control for the directed complex dynamical net-works with multi-links are investigated. By applying control strategies to a small fraction of nodes, the pinning feedback controllers which are less conservative are derived to make the directed (undirected) complex dynamical networks with multi-links synchronize. Moreover, the problems of designing controllers are converted into solving convex optimal problems of a series of linear matrix inequalities. The solution can be obtained by the available soft wares, which reduces the complexity to solve the question. Then we improve on the determinant method of pinning synchro-nization which is easy to realize. Numerical examples are provided to demonstrate the effectiveness of the pinning synchronization controllers.(3) The problems of synchronization analysis and control for a more general model of complex dynamical network with coupling delays and delays in the dynam-ical nodes are studied. Based on the theory of Lyapunov stability combined with linear matrix inequalities technique, synchronization criteria are derived. Using the theory of Lyapunov-Krasovskii functional, linear feedback controllers are designed for the case where the coupling coefficients are known. Considering the fact that it is often difficult to get exact estimation of coupling coefficients in reality, the adap-tive feedback synchronization controllers which have strong robustness are given when the coupling coefficients have nonlinear perturbations or unknown bounded nonlinear functions. It should be pointed out that the dynamical nodes need not satisfy the very strong conditions and the coupling matrices are not assumed to be symmetric or irreducible.(4) The problems of robust stochastic control for the networked control sys-tems are investigated. Based on the theory of stochastic control and the theory of Lyapunov stability combined with linear matrix inequalities technique, sufficient conditions about robust stochastic exponential mean square stability are derived for networked control systems with the effects of the networked-induced time de-lay, data package dropout, package time sequence confusion, parameter and outer stochastic perturbations. We divide the parameter uncertainty into two parts, one is uncertainty in the general form, and the other is Wiener process. Then we can fully use the known condition and improve the performance of system and the max-imum allowable transfer interval(MATI). The passive control and H∞control are introduced into the stochastic networked control systems, respectively. The robust stochastic passive controller and H∞controller are designed. Numerical simulations are demonstrated to show the effectiveness of the analysis methods and controllers.