Controllability Analysis Of Multi-agent System Based On Partition

The controllability of multi-agent system is a hot issue in today’s society.Solving this problem will help to give full play to the application of artificial intelligence projects in various fields.This paper mainly studies the controllability analysis of multi-agent system based on equivalence partition,and focuses on the controllability problem of the system when automorphism and symmetry exist in the topological structure.Based on the existence of special structure,the controllability effect of breaking the internal structure of the system on the system is studied.This paper will elaborate on controllability based on partition,so as to lay a theoretical foundation for solving the practical problem of controllability of multi-agent system.This paper reviews many researches on controllability of multi-agent systems in recent years and puts forward the important theoretical value and practical significance of controllability research.Using the graph theory and matrix algebra theory and other research techniques and tools,analyzes the problem,puts forward the topological structure of special internal contact(Automorphism and leader symmetry)system controllability during analysis,so as to exclude the special figure(figure)in the choice of the leader of the system is not controllable node,as well as the system’s rough almost equal division of controllability problems.The controllability analysis of undirected graph based on partition is introduced in detail.Through the analysis of graph theory,controllability is analyzed in topological structure with automorphism,and the necessary conditions for controllability are given.By analyzing the relationship between automorphism and leader symmetry in the system,we can make full use of the known conditions to complete the reasoning of algebraic relation in the connection graph,thus eliminating the leader choice that makes the system uncontrollable.In combination with the above work,the sufficient and necessary conditions for the symmetry of the leader making the system uncontrollable are proved,and a new method is added to the research on the controllability of the system.In the research based on directed graph,the controllability of directed graph is analyzed,the equivalent division of directed graph is proposed and the rationality of definition is proved.This paper expounds the influence of different control inputs on the controllability of the system,finds out the necessary conditions for the coarsiest almost equivalent division of controllability,and proves that a method can be found to break the resulting symmetry and then exclude the leader option that makes the system uncontrollable when there is a symmetric structure in the system.