Controllability Analysis Of A Multi-agent System Under Topological Edge Additio

As an important part of distributed network control,the controllability of multi-agent system plays an important role in the development of artificial intelligence,therefore,it has become one of the hottest research directions in the current society.Based on the leader-follower system model,the thesis uses the matrix theory and graph theory to study the controllability of multi-agent system with adding edges under two topologies,directed and undirected,respectively.The main content is divided into the following parts:Firstly,under the directed and undirected topologies,the specific connection relationships making the system controllability maintained in a single topology structure are given.Furthermore,the multi-topology construction rules where controllability of the two topologies can be ensured are built based on single topology structure,which provide an important basis for the construction of complex topologies through simple topologies.Secondly,under the directed topology,for directed paths and directed paths with adding edges,the controllability of multi-agent system is studied by using algebraic methods.According to the directions,the added edges are divided into reverse edges and forward ones.And then,combined with the difference between the leader node and the follower node,the added edges are further divided into four cases,and the corresponding controllability conclusions are obtained in each case,which provide a new method to judge the controllability of directed paths with adding edges.What’s more,a construct method for a class of controllable directed topologies is proposed on the basis of multi-topology construction rules which can make controllability maintained.Finally,under the undirected topology,for undirected paths and undirected paths with adding edges,the controllability of multi-agent system is studied from the perspective of graph theory,and the special situation of the non-trivial cell in the topology caused by adding edges is analyzed by taking advantage of the equitable partition.Due to the fact that edges has no directions and the difference between the leader node and the follower node in the undirected topology,the added edges are divided into two cases,and the relevant conclusions about the non-trivial cell are obtained in each case.In addition,the thesis discusses the relationship between the existence of non-trivial cell and the controllability.According to the characteristics of non-trivial cells,the concept of state-equitable nodes is proposed,and an edge addition method that can make any two nodes in the undirected path become state-equitable nodes is brought forward.Specially,we give two algebraic conditions for determining the controllability of multi-agent system after adding edges to the undirected paths from eigenvalues and eigenvectors respectively.