Research On The Controllability Of Directed Complex Networks Based On Driving Nodes

The ultimate purpose of studying complex networks is to control it.In the past decade,scholars have been focusing on how to control some nodes in the network so that they can be driven to the desired state,that is,we want to control the state of each node in the network.In order to achieve complete control of the network,we need to consider the following points.That is,to determine whether the system is controllable,how to add external input to make it fully controllable,and the minimum number of nodes needed to control the network achieving fully controllable.From the perspective of graph theory,the relationship between controllable performance and topological structure of complex networks is analyzed and discussed.Combining with the Lin structural controllability,the thesis gives the necessary and sufficient conditions for the structural controllability of complex networks.By using the matching method and the minimum input theorem,we obtain that the minimum controlled nodes set of the system is the union of the minimum unmatched nodes set and the minimum unreachable nodes set.Then,combining with the PBH rank criterion,the exact controllability of complex networks is proposed,which provides a complete theoretical framework for studying controllability of the network with arbitrary topology structure and determinate link weights.By analyzing the exact controllability of complex networks and the node control ability,the optimal minimum driver nodes set for the complete controllability of the system is determined.Finally,the structural controllability of edge dynamics in complex networks is given.When studying the structural controllability of the edge dynamics system,the controllability of the edge dynamics system is summarized by transforming the edge dynamics system into the nodal dynamics system and analogizing the controllability of the nodal dynamics system.The thesis focuses on the influence of the network topology on the controllability of the system.From the viewpoints of structural controllability,exact controllability and edge controllability,the relationship between the controllability of the system and the network topology,the relationship between the network of arbitrary topology structure and determinate link weight and the driver nodes,and the influences of the external input on the the controllability of system are discussed respectively.