Controllability Classification Of Graphs In Multi-agent Network Systems

The multi-agent system is an emerging interdisciplinary,which has caused great attention of academia both at home and abroad.Controllability is becoming a focus problem in the research of the multi-agent system.And it is the core and foundation of the multi-agent system.In this paper,the main research contents and contributions are as follows:First,the background and significance of the multi-agent system are summarized,as well as the related knowledge in graph theory and matrix theory.And the controllability criterion of the multi-agent system is introduced.Second,mainly study graph controllability classes in the multi-agent system,and divide into two cases: the single signal and multi-signal input system,and each includes essential controllable graphs,completely uncontrollable graphs and conditional controllable graphs.Each classification is analyzed and studied to solve the problem of the characteristics and properties of graph controllability classes.Furthermore,the criterion of controllability is extended,and the relationship between graph and the controllability could be more clearly understood.Third,the difference between the case of single signal input and the multi-signal input is described.And the extension and transformation of multi-agent system model are provided based on the Laplacian matrix.And in the special case of the threshold graph,the difference between single signal input and multi-signal input is analyzed and compared.