Research On Adaptive Synchronization And Control Strategy In Complex Networks

Complex network has attracted more attention because it can character more real systems. Based on Lyapunov stable theory and matrix theory, synchronizatin and control in complex networks as well as parameter identification of chaotic system are discussed in this thesis.Firstly, global synchronization in adaptive coupling networks is studied. A new simple adaptive controller is proposed based on a concept of asymptotically stable led by partial state variables. Under the proposed adaptive update law, the network can achieve global synchronization without calculating the eigenvalues of the outer coupling matrix. The update law is only dependent on partial state variables of individual oscillators. Numerical simulations are given to show the effectiveness of the proposed method, in which the unified chaotic system is chosen as the nodes of the network with star coupling and ring coupling.Secondly, we investigate the pinning control strategy of BA scale-free network through numerical analysis. A new cost function is defined to measure the cost of pinning control. Compared the control gain and cost of pinning"smallest"nodes and"biggest"nodes, an interesting result that a smaller control gain and a lower cost are guaranteed by using the control scheme of pinning nodes with smallest degrees is achieved. Moreover, there is a minimal control cost by pinning"smallest"nodes and"biggest"nodes, respectively. That is, we have optimal control gain. The number of controllers by pinning the"smallest"nodes is considered in the end.Finally, the method of parameter identification of chaotic system based on unknown parameter observer is extended to non-autonomous systems. Some observers for Van der Pol-Duffing system are designed and the unknown parameters are identified using them. The simulations demonstrate the effectiveness and feasibility of the improved approach.