Controllability Analysis Of Multi-agent System Based On Equivalence Partition

Controllability is a fundamental problem in the study of multi-agent systems has attached wide attention.This paper mainly studies the controllability of multi-agent systems based on leader-follower dynamics.We use graph theory to characterize the controllability of the system in the case of single leader and multi-leaders respectively.In particular,the influence of the selection of leaders on the controllability of the systems under various topological structures is mainly introduced.The main contents and contributions of this paper are as follows:Firstly,the background significance and development status of multi-agent systems are summarized systematically,and the basic knowledge related to the research is elaborated.The relationship between the classical model of linear system and the leader-follower structure model considered in this paper is introduced and deduced in detail.In the study of the controllability of multi-agent systems with single leader,the theoretical criterion of system controllability is given by using the properties of eigenvalues and eigenvectors of Laplacian matrices of systems.The relationship between automorphism and symmetry of topological structure is analyzed.The influence of leader selection on system controllability is analyzed from the graph structure,and the methods to avoid the uncontrollability of systems are given.In the study of the controllability of multi-agent systems with multi-leaders,the upper bound of the controllable subspace of the system is characterized by equitable partition and almost equitable partition.The relationship between the controllability of the system and the topological structure of the graph based on equitable partition is given,which provides a method of judging the controllability of the systems based on graph theory.The conclusions and limitations of controllability of general systems based on equitable partition are analyzed in detail.A special kind of topological structure is proposed,and the conditions for the controllability of the systems are given.