On Pinging Synchronization Control Methods For Complex Networks

With the rapid development of computer science and network theory, the study of complex networks attracts more and more attention of experts and scholars from various fields. Complex network has become highly active, with many new systems being proposed in application areas ranging from math to biology and computer science. Synchronization problem is one of the most demonstrating topics in complex networks. Synchronization phenomena, as a basic character of complex large-scale systems, is ubiquitous in the natural systems and man-made systems such as:biology, engineering and mechanics. Therefore it is great significant to study synchronization control problem of dynamical systems on complex networks. In this dissertation, combining the nonlinear system theory, control theory and matrix analysis, the synchronization of complex dynamical networks is investigated. The main work can be summarized as follows:Firstly, considering a class of coupling complex network, a sampled-data controller is designed with pinning control strategy. The sampled system is described by input delay approach. Numerical simulation results show that the proposed controller can achieve synchronization for the complex network with many Lorenz chaotic systems as its nodes. Then the synchronization effect is analyzed on the influence of coupling strength, degree of the controlled nodes and the number of controlled nodes.Secondly, the pinning sampled-data synchronization control problem of complex networks with coupling delay is investigated. For the complex network with time-varying delay, a sufficient delay-dependent stability condition is given by applying linear matrix inequalities and Lyapunov stability theory. Numerical simulation results show the effectiveness of this method. In addition, the synchronization performance on the influence of coupling strength, degree of the controlled nodes and the number of controlled nodes is illustrated by numerical simulation.Thirdly, for a class of complex network with both coupling delay and node delay, an adaptive pinning controller is designed. The stability of the dynamic error system is proved by Lyapunov theory. Numerical simulation results show the effectiveness of the designed controller.Finally, the main work of this dissertation is summarized and some future research directions are put forward.