Research On The Controllability Of Several Types Of Topological Structures Under The Confrontation Network

In recent years,signed networks have a concern in the community about the network control as they allow studying antagonistic interactions in multi-agent systems(MASs).Controllability is an essential property in the research of system control,so the study of controllability under multi-agent systems is of great significance.This article meanly attaches importance to:First,it describes the research background of multi-agent systems,as well as the mathematical tools and theoretical foundations used in the research.Second,the leader-follower structure proposed by Tanner(2004),is introduced in the network with antagonistic interactions,and the necessary conditions for the controllable network are given.The general almost equitable partition under the confrontation network is described.Third,the controllability of a class of signed complete graphs is studied.Based on hypothesis,a sufficient condition for the control of a class of signed complete graphs is given.Moreover,an analysis about the controllability problems of the Peterson graph with antagonistic interactions is proposed under the partition of three-partite graph.Fourth,we put forward a concept of perfect controllability,which means that a multi-agent system is controllable with no matter how the leaders are chosen.In this situation,both the number and the locations of leaders are arbitrary.A necessary and sufficient condition is derived for the perfect controllability.Moreover,a step-by-step design procedure is evidenced by which topologies are constructed and are verified to be perfectly controllable.The principle of the proposed design method is interpreted by schematic diagrams along with the corresponding topology structures from simple to complex.