Controllability Analysis Of Multi-agent Systems Based On Partition Theory

In the related research of multi-agent,the controllability of multi-agent is one of the the hottest research directions.As the development focus of contemporary artificial intelligence,solving this problem is conducive to promoting the development of intelligence in various fields.In this paper,based on the leader-follower mathematical model,with the help of graph theory,matrix theory and controllability criterion,the controllability of multi-agent system in cooperative network and counter network is studied by using equitable partitions.The main content is divided into the following parts:Firstly,this paper introduces the research background and significance of multi-agent system as well as analyzes the research status of controllability of multi-agent system.We elaborate the theoretical knowledge needed to study the controllability of multi-agent system,and give the leader-follower model to prepare for the controllability analysis of multi-agent system.Secondly,in cooperative network,the necessary conditions for judging the controllability of the system are given by using equitable partitions to select any nontrivial cell as the leader.Based on the four-node undirected graphs,the complete characterization of controllability graph theory is completed,and the four-node topological graphs are extended to general topological structure.By analyzing the controllability of all kinds of topological graphs,it is found that two kinds of equitable partition tools can not judge the topological structure of the system controllability.The limitation of equitable partition for judging system controllability is analyzed in detail,and the algebraic requirements for establishing the sufficient and necessary conditions of the system controllability are given.Then,in counter network,based on the general almost equitable partitions and invariant subspace,the relationship between the dimension of controllable subspace and the number of cells is obtained,and the conditions for judging the controllability of the system are given by derivation.Finally,in the comparative analysis of multi-agent systems in cooperative networks and counter network,the different number of equitable partition in the two networks are given.At the same time,the necessary conditions for determining the controllability of confrontation topology are obtained by using structural balance and leader symmetry,and the equivalence of the two kinds of network controllability determination under certain leader selection is obtained by comparison.