The Fast Consistency Of The Multi-agent System And The Controllability Problem Under The Equivalent Partition

In recent years,artificial intelligence has been the frontier of sciencific research with multi-agent system being one of its important branches.Consensus and Controllability problems have been the key issues in the research of the multi-agent system.In this thesis,the main research contents and contributions are as follows.First,the background and significance of the multi-agent systems are summarized,as well as the related knowledge in graph theory and matrix theory.The dynamic model and control laws of multi-agent systems are introduced.Second,we introduce a superposition system to superpose to the original system,and study the corresponding variations of the convergence rate.By analyzing the eigenvector of ?₂?L?,results are derived on checking whether the convergence rate can be changed.Under fixed cost,by taking advantage of the inequality of eigenvalues,conditions are derived to achieve the largest convergence rate with the largest delay margin,and at the same time,the corresponding topology structure is characterized in detail.Based on equitable weights partition and almost equitable weights partition,a method of constructing invalid algebraic connectivity weights is proposed to keep the convergence rate unchanged.And simulations are given to demonstrate the effectiveness of the results.Third,we investigate the controllability by equitable partition.We mainly analyze the proposition of nontrivial cells,and give the necessary condition for controllability.By analyzing the completely connected nontrivial cells and incompletely connected nontrivial cells,we give the different conditions for different cases.In addition,we show that there are special formats of the eigenvectors of L,which indicates the topology can affect the algebraic situation of L.Fourth,we use PBH condition to analyze the controllable subspace,and give the sufficient and necessary conditions for controllability under minmum inputs.