Study On Synchronization Control Of Complex Networks

Human society has entered a complex network era with the rapid development of network information technology. In today’s world, network began to spread into our life, that is to say, we already can’t be separated from network. Every day, we are enjoying various service the network provides for us. From the point view of topology, most of the systems in our life may be abstracted as the complex networks. The extensive study on complex network is pervading sciences and engineering today, from physical, technology, biological, to social sciences. Because of this, along with complex networks progress and the development, synchronization problem achievement vital realistic question becomes the multitudinous discipline research day by day the hot spot. Therefore it is potentially of great significance to investigate synchronization control problem of dynamical systems on complex networks.In this dissertation, based on the research on synchronization of continuous-time coupled dynamical networks and its application, different types of complex networks, i.e., the chain network, the small-world networks and the spatiotemporal dynamical networks are investigated. As we all know, a complex network normally has a large number of nodes. To reducethe number of the controllers, a natural approach is to control a complex network by pinning part of nodes. The main contributions of this dissertation are summarized as follows:(1) Focusing on the chain complex networks systems, the concept of sliding mode synchronization approach by only one control input is presented. The only control input in the last node of chain complex networks is investigated and the criterion of synchronization is obtained. The double-scroll circuit chaos systems are treated as nodes and the network is constructed with the state variable coupling. By selecting a switching sliding surface, the chaos synchronization of network is achieved with one control input only. The stability analysis and the numerical simulations demonstrate that the complete synchronization in chain network can be realized for all nodes. Finally, concrete conclusions are arrived which are more suitable to the application.(2) The outer synchronization of irregular coupled complex networks is investigated with nonidentical topological structures. The switching gain is estimated by an adaptive technique, and a sliding mode controller is designed to satisfy the sliding condition. The outer synchronization between two irregular coupled complex networks with different initial conditions is implemented via the designed controllers with the corresponding parameter update laws. The chaos synchronization of two small-world networks consisting of N uncertain identical Lorenz systems is achieved to demonstrate the applications of the proposed approach.(3) A second-order terminal sliding mode controller is proposed for outer synchronization of a class of complex networks with disturbances. This control scheme adopts a hierarchical control structure to reduce the numbers of controllers. The multivariable error systems were decomposed into two subsystems, a controllable nonlinear subsystem and a linear subsystem. The proposed terminal sliding mode ontroller was only designed for the nonlinear subsystem. The linear subsystem is set to appropriate sliding mode parameters to implement synchronization. This approach possesses the features of less controllers, faster convergence and higher tracking precision.The performance of the control strategy is evaluated through the control of the complex networks consisting of N identical R?ssler systems. Simulation results demonstrate the effectiveness of the proposed control method.(4) A backstepping scheme is proposed for synchronization between two complex dynamical networks with different structures. The nodes of the networks are spatiotemporal chaotic systems. A recurrence relation containing the information from neighbors is established so that only one control input is needed to synchronize two spatiotemporal networks. The Lyapunov stability theory is applied to prove that the differences between the drive and the response networks tend to zero asymptotically under the only control. Therefore, this method provides a new way for the network synchronization.