Adaptive Synchronization Of Complex Networks And Its Application

Recently, with the rapid development in computer technology, communication technology and so on, researchers from various fields have paid more and more attentions to the study of complex networks. The main purposes of the investigation of complex networks is to find the relationship between the network structure and its function and consequently to design some effective strategies to improve the networks’ performance. The pinning control strategy means only a small fraction of nodes informed from the objective and the adaptive strategy which can regulate the networks’parameters according to its performance as well as the intermittent control strategy, that is, it needn’t to receive the external input information persistently have been introduced into this paper. The main contents and the innovations of this paper are stated as follows:1. The adaptive synchronization of first-order complex networks without time delay and with time-varying delays on fixed topology is investigated, respectively. By introducing effective distributed adaptive strategies to both the coupling strengths and the feedback gains, we have got that:all nodes of the connected system can converge to the desired state even though only one node is pinning controlled, don’t need to know the global information and to solve any LMI. For a huge system, it is difficult to obtain the global information of the system, and these distributed adaptive strategies update the corresponding parameters according to the node’s neighbor information only, and needn’t to know the global information, this is also the superiority of the distributed adaptive strategies comparing to the central adaptive ones.2. Adaptive synchronization of first-order complex networks on switching topology is discussed. In this paper, we study this problem by using the methods of differential inclusion and non-smooth analysis. What’s more, the nonlinear dynamics only asked to satisfy the locally Lipschitz condition but not the globally Lipschitz condition. By designing rational adaptive strategies to the coupling strengths and feedback gains, we get the conditions that make the system realize synchronization and acquire the finally convergence region of the related parameters.3. Adaptive consensus of second-order complex dynamical networks with time-varying delays and virtual leader has been considered. Yet, all nodes and the virtual leader share the heterogeneous nonlinear dynamics which satisfy the global Lipschitz condition. For a connected system, we discuss the synchronization of the symmetric and the asymmetric weighted coupling configuration matrix respectively in detail via introducing adaptive strategies to the coupling strengths and the feedback gains of both the position and velocity, and gain that the position and the velocity of each node can converge to those of the virtual leader even when only one node is pinning controlled. 4. The periodically intermittent pinning control of second-order delayed multi-agent systems has been investigated. For the second-order delayed multi-agent systems where all agents and the virtual leader share the same nonlinear dynamics, at first, we study the synchronization of this system in each time period by means of intermittent pinning control, then we get the criteria which drive all the agents to achieve exponential synchronization by mathematical induction.