Pinning Control And Optimization Of Complex Networks

Complex networks is an interdiscipline involving mathematics,physics,control science,sociology,economics and many other disciplines.At present,the research on the control of complex networks has become a hot issue,attracting experts and scholars in different fields to carry out related in-depth research.Controllability of complex networks is a hot direction in the research of complex network control.The ultimate goal of our research on the controllability of complex networks is to control the system from the arbitrary state to any desired state by exerting external signal on some nodes in the network.In order to fully control the network system,we must first determine whether the network system can be controlled.If it is controllable,we should further identify the minimal number of driver nodes.On the other hand,many scholars have concerned synchronization of complex networks,which is widely existed in nature and society.In recent years,with the discovery of the small-world and scale-free features of complex networks,researchers began to combine the nodes dynamic with the structure of networks to study the synchronization behavior of networks.Based on previous research,this paper studies the controllability,synchronization,and optimization of complex networks with the help of graph theory,control theory,nonlinear system theory,and matrix theory.In this paper,the controllability of edge dynamical systems in complex networks is firstly studied.The edge dynamics model is given for unidirectional circular networks,and the necessary and sufficient conditions for the control of edge dynamics are deduced.Then,the problems of pinning synchro-nization and optimization for complex dynamical networks with sign inner-coupling configurations are investigated in this paper.Due to the negative interactions between the node variables,some new ragged synchronized regions are discovered for the chaot-ic Chen system.A modified optimization algorithm of weight assignment in arbitrary networks subjected to pinning control is developed.It is shown that the synchronizabil-ity of the pinned network can be effectively improved by reassigning the edge weights.