Unstable Equilibrium Points Stabilization Of Complex Dynamical Networks Using Pinning Control

In this dissertation, the stabilization of unstable equilibrium points for a complex dynamical network is addressed by using pinning control method. Compared to the global control scheme widely used in previous studies, pinning control can achieve the same goal with a simple controller, showing important theoretical and application values. The main research work is as follows:First, for the state coupled complex network model, a controller is proposed for stabilizing the unstable equilibrium points of the network by using output signals of partial nodes of the network. The controller parameters are designed based on Lyapunov stabilization theory. Simulations are given for global coupling network, the nearest neighbor coupling network, the scale-free network and the small-world network, showing the effectiveness of the proposed method. Next, based on the output feedback pinning control, we compare output coupling networks with state coupled networks for choosing the number of nodes of construe under different network toplogies.Second, for the output coupled network model, a controller is proposed for stabilizing the unstable equilibrium points of the network by using state signals of partial nodes of the network. The controller parameters are designed based on Lyapunov theory. Simulations are also given for global coupling network, the nearest neighbor coupling network, the scale-free network and the small-world network, showing the effectiveness of the proposed method. Next, based on the state feedback pinning control, the state coupling networks and output coupled networks are also compared to choose the number of nodes for construe under different network topologies.Third, the methods for optimally choosing nodes of construe are studied for different network topological networks, and we compare these methods with the two methods-degree based and randomly selection, showing that the proposed methods herein have some advantages.