Controllability Analysis Of Multi-agent Systems With Strongly Connected Input Component

With the development of society,multi-agent system fully embodies the advantages of being more convenient and intelligent than a single system in practical applications,so it has become one of the hottest research directions in today’s society.In this thesis,the controllability of multi-agent system with input strongly connected component is analyzed in depth with the help of graph theory and its partitioning tools,matrix theory and other basic knowledge.The main research contents are divided into the following parts:Firstly,a new graph partitioning tool is proposed to input strongly connected component(Input strongly connected component,In SCC).By using PBH criterion and other tools,the controllability of multi-agent system with In SCC structure and the controllability of topology structure composed of In SCC and road map are analyzed,and the leader selection method is given to achieve system controllability.Then,the controllability of the undirected topology corresponding to the multi-agent system that only contains the In SCC structure is studied by using equivalent partitioning and other tools,and compared with the directed topology,it is concluded that the In SCC structure proposed in this thesis is more advantageous to construct the controllability map.Finally,based on the In SCC structure,the communication edges are added to different In SCC structures and roadmaps,and it is proved that adding communication edges in a certain way does not change the controllability of the multi-agent system,which lays the foundation for the construction of the energy-controlled graph.Secondly,the multi-agent system containing only the In SCC structure is studied in terms of controllability after the edge is damaged.Based on the theory of multi-agent control system,a new method is proposed to identify different types of edges in the multi-agent system by combining the state space model and the knowledge of graph theory.According to the situation that the edges in the system suffer damage and fail,they are classified into three types and four different combination types,and the algorithm to identify different types of edges is given.In addition,the laws of edge failure on system controllability and Laplace matrix rank for a multi-agent system containing only In SCC structure are given.When different types of edges fail,the leader selection is given to ensure that the multi-agent system containing only the In SCC structure is controllable.Finally,how to construct the energetic control graph is discussed,and the energetic control problem of the multi-agent system containing only In SCC structure under switching topology is investigated.Based on the properties of the In SCC structure,on the one hand,the energy-controlled subspace of the complex topology is estimated,the lower bound of the dimension of the energy-controlled subspace is obtained,and the construction method of a class of energy-controlled topology is proposed.On the other hand,considering that the multi-agent system under fixed topology cannot solve many practical problems and the multi-agent system may be time-varying,the controllability of the multi-agent system containing only the In SCC structure under switching topology is analyzed and the sufficient conditions are given.