Controllability Analysis Of Multi-agent Systems In Complex Scenarios Based On Graph Theor

Controllability is not only the basic problem of control theory but also the core problem of multi-agent system performance analysis.This thesis analyzes the controllability of multi-agent systems in various complex scenes with the help of graph theory,matrix theory,and other basic theories.Some controllability criteria for multi-agent systems in complex scenes are obtained,which combine the advantages of algebraic conditions and graphic conditions.The main contents and results are as follows:Firstly,this thesis describes the research background and research status of multi-agent system controllability,the existing results and directions of the research on the controllability of multi agent systems are summarized,and the preliminary knowledge and symbols are introduced.In order to deal with the complexity at the level of individual dynamics,two complex situations including general linear characteristics of agents and different dynamic representations between agents are discussed respectively based on the signed network,and some new definitions of equitable partition are given respectively too.The controllability of the corresponding systems is discussed and some graph theoretic criteria of controllability are obtained.At the same time,the relationship between the controllability of the originally signed network and the controllability of the corresponding unsigned network is discussed.In order to deal with the complexity at the level of communication,some new definitions of equitable partition are given based on the signed network.The controllability of the system with single delay and multiple delays is discussed respectively.Some graph theoretic and algebraic criteria for controllability are obtained.In order to deal with the complexity at the level of network properties,some new definitions of equitable partition are discussed based on matrix weighted signed network.Two complex cases including fixed topology and corresponding switching topology are discussed,and some graph theoretic criteria for controllability are obtained.