Multiple Body System Controllability Analysis Based On Directed Tree Topology Map

The controllability of multi-agent is a hot topic in the controll field,the multi-agent system with a specific topolgy is a very important content.This paper studies the controllability of multi-agent under the directed tree topology.The main contents of this paper are as follows:Firstly,some basic contents of graph theory and matrix theory were introduced.In the aspect of the graph theory,the concepts of directed graph,undirected graph and weight were introduced,and the establishing process of the system model was described in detail.In the aspect of the matrix theory,we mainly introduced the degree matrix,adjacency matrix and laplace matrix,introduced the relationship between them,and gave some spicific examples.The model of the multi-agent system with directional tree was established,and given the necessary and sufficient conditions for the system control.A new model transformation was carried out by the star transform matrix,and pointed out the necessary and sufficient conditions under the new model which can make the system controllable.Finally,analyzed the controllability of road map and star graph by the new obtained necessary and sufficient conditions.The model of non-uniform multi-agent system with directed trees was established.Through the matrix property,the rank criterion was simplified and the necessary and sufficient conditions for system control were discussed by the final form of rank criterion.The conditions that make the system controllable were pointed out by some spicific examples,and gave some suggestions to improve the system controllability.