The Synchronization Control And Its Applications Of Complex Networks With Coupling Time-delay

Complex networks are widely applied in nature, society and engineering, which have attracted much attention from researchers in various fields. The synchronization phenomenon is widespread in various complex systems. It is one of the most typical dynamic characteristics of complex networks, which is also the foundation of cooperation in complex systems. The investigation of synchronization for complex networks can not only help people to realize the causes of formation of some phenomena in the nature, but also provide us with some new ideas and methods in dealing with complex large systems. So the synchronization of complex networks has a broad application prospect, and the research for the synchronization of complex networks has important theoretical and practical significance.The synchronization control of several classes of complex networks with coupling time-delay is investigated in this thesis based on Lyapunov stability theory, matrix theory, control theory, graph theory and Linear Matrix Inequality (LMI). The main contents of this thesis are summarized as follows.1) The synchronization problem for Lur’e type complex networks with switching topologies and coupling time-varying delay is investigated based on Lyapunov-Krasovskii stability theory. Some synchronization criteria and control solutions are derived in terms of LMIs. What’s more, high dimension LMIs of the criteria are decoupled into a set of low-dimension ones by using an eigenvalue-decoupling method and convex optimization theory, which significantly reduces the computation complexity of the criteria.2) Based on Lyapunov-Krasovskii stability theory and LMI method, H∞ synchronization control for a class of complex networks with time-varying coupling matrix and coupling time-delay is investigated. A criterion is proposed to decide the Hoo synchronization of complex network with time-varying connection, and a Hoo decentralized feedback controller is designed to achieve asymptotic synchronization for this kind of networks. In addition, high dimension LMIs of the derived results are transformed into a set of low-dimension ones by using the convex optimization theory and a proposed lemma, which can deal with the time-varying coupling matrix and reduce the computation complexity.3) The synchronization control of a time-varying complex network with non-identical nodes as well as coupling time-delay is investigated. Combing with the ideas of entrainment control and feedback control, we designed two efficient control schemes to synchronize the network onto any given smooth goal dynamics. By using the Lyapunov-Krasovskii stability theory, the correctness of the proposed schemes is proved.4) Considering that each node in a heterogeneous complex network has different goals, the concept of individual synchronization is proposed. Based on the idea of compensation and feedback adjustment, two kinds of hybrid control scheme are proposed for complex network without coupling time-delay and with coupling time-delay respectively. The correctness of the control strategies are proved by using the Lyapunov stability theory.5) The network-based leader-following consensus problem for second-order multi-agent systems with nonlinear dynamics is addressed. By modeling the consensus problem of multi-agent system into the synchronization problem of complex network with coupling time-delay, we applied the theory of synchronization for complex networks into the consensus problem, and derived a sufficient condition to design network-based controller to make the followers reach consensus with the leader for second-order multi-agent systems with nonlinear dynamics.6) The coordination control of a supply network with time-delay is investigated. By applying the theory of synchronization control for complex networks to the supply network, a feedback control strategy is derived, which can make the complex supply network work at the desire state.