Selection And Application Of Driving Nodes In Complex Networks

In recent years,the problem of controllability of complex networks has become a hot topic for many researchers from the modern network engineering control field.Controlling the complex networks is crucial in science and engineering,and controllability is an important attribute of the control system.The main contents of this paper as follows:First,The basic knowledge and basic concepts of the research on controllability of complex network systems are briefly introduced.In addition,the main theories for studying the controllability of complex networks are described.Second,We pay attention to find the optimal minimum driver nodes set with more stronger control ability to achieve the controllability of complex networks by using the methods arising from graph theory and matrix theory.Firstly,we determine the minimum number of driver nodes;Secondly,the optimal minimum driver nodes set is determined by searching the optimal connection added between new control signal and state node with more stronger control ability.Finally,the input signals are added to the optimal minimum driver nodes to complete the controllability of the network.In the study,the algorithm of the optimal minimum driver nodes set is also designed for the controllability of complex networks.Third,it is difficult to control the huge network and it is not necessary to achieve full controllability.Therefore,in this paper,we mainly consider controlling the target nodes in the network.We first analyze the target control of directed networks with single input.Then the greedy algorithm is optimized and it is applied to the target control of multi-input directed network,and the immune greedy algorithm is proposed at the same time.Fourth,it mainly explores the edge controllability of complex networks.For a complex network whose dynamic process is defined by edges,the controllability of the network is optimal if complete controllability of the network can be achieved by applying an input signal to any non-isolated vertex.The edge controllability of the network is realized by designing the two strategies,including adding-edge strategy and turning-edge strategy.The analysis of the classical cases shows that the two methods are all feasible and effective.