Research On Adaptive And Pinning Synchronization Control Of Complex Networks

The Complex network is an emerging discipline of the complex system. It has attracted more and more attentions from various fields of science and engineering, and has become a popular research topic. Complex networks have been applied in different areas ranging from physics to biology, from science to computer sci-ence. The Synchronization phenomenon, as a typical collective behavior of complex networks and one of the most demonstrating topics in complex networks, possess great potential to investigate the problem of synchronization in complex dynamical systems.This dissertation studies the problem of synchronization control of complex dy-namical networks, including inner synchronization and outer synchronization. Based on the stability, differential equation, matrix, control and graph theory, the meth-ods of state feedback, adaptive control, pinning control and periodically intermittent control have been employed to investigate the synchronization of several kinds of continues time coupling systems. Numerical simulations are given to illustrate the effectiveness of results. The main contents are listed as follows:1. The synchronization problem for an array of coupled networks has been stud-ied. The study provides some simple criteria, which are easier than the linear matrix inequality method. In addition, a method of using the scalar signal as the coupling signal is proposed aiming at the huge information transmission characteristics. This method does not only simplify the relationship of states variables between every two coupling nodes of complex networks, but also save the channel resources during the processing of information transmission, and thus gains economic efficiency.2. The synchronization problem for one type of uncertain time delay coupled complex network has been investigated. With the help of stability theory and adaptive control technique, some adaptive feedback controllers are designed to make the complex network achieve asymptotic synchronization fast. In addition, there is no restriction on the coupling matrix with symmetry, and no need for the inter coupling relation to keep consistency with each other.3. Lag synchronization between two general complex networks has been re-searched. Using the adaptive pinning control method, some criteria are ob-tained to keep the drive and response system with constant coupling strength to achieve lag synchronization. In addition, an effective pinning controller has been designed for the outer synchronization of drive and response systems with adaptive coupling strength. The criterion considers the relationship a-mong controllers numbers, the coupling strength and the controller gain, and has important realistic significance in engineering design.4. Lag synchronization between two complex networks with different nodes and different topological structures has been studied. Based on the observer theory, invariant set theory, and adaptive technique, some criteria are given for the lag synchronization between drive and response systems. The application of observer theory makes the number of coupled variables among nodes flexible. It simplifies the network structure, and resolves the problem of transmission congestion of signals at the same time.5. The synchronization problem for drive and response system is investigated by adaptive periodically intermittent pinning control. Based on the stabili-ty theory, differential equation theory and adaptive technique, some criteria are obtained. Moreover, the criteria for synchronization between drive and response systems with time delay also have been received by adaptive period-ically intermittent pinning control. This method combines the advantage of pinning and periodical intermittent control, and can reduce the energy con-sumption greatly.