The Overall Controllability Of Multi-agent Systems And The Influence Of External Control Input Methods On The Controllability Of Single-stage Systems

In the multi-agent system problem,the primary problem to be solved is controllability.This article will use graph theory and matrix theory,combined with the two major models describing multi-agent systems,to further study and analyze the overall controllability of more general multi-agent systems.The reason why the same multi-agent system will show different controllability under different external control input methods is studied.The main content is divided into the following parts:First,we introduce the research background and basic problems of the controllability of multi-agent systems,and expound the basic knowledge and theoretical foundation needed to study this problem.We analyzed the two main forms of the current single-order continuous-time multi-agent system model,and deduced the relationship between the two in detail.Based on the single-order model,a more general multi-agent linear system model is summarized.The relationship between the controllability of the network topology and individual dynamics in the general multi-agent system and the overall controllability of the system is studied.The sufficient and necessary conditions for the overall controllability of the system under the general model are obtained.Finally,for a class of special systems,a method to judge that the system cannot be controlled is given.For the single-order multi-agent system,the influence of two different external input methods on the controllability of the multi-agent system,such as one external input affecting multiple leaders and one external input affecting one leader,was studied.The reason why the same system exhibits different controllability under different external input methods is explained.Regarding the special case of one of the input methods,it is concluded that the undirected graph under the single-order multi-agent linear model cannot be controlled under the broadcast signal.Regarding the special case of one of the input methods,it is concluded that the undirected graph under the single-order multi-agent linear model cannot be controlled under the broadcast signal.According to the characteristics of feature vectors,the leader selection method that makes undirected road graph and undirected loop graph uncontrollable under two different external input methods is given.Finally,the issue of whether the external input signal can be used as a virtual node was elaborated,and related conclusions were obtained.