Sign-Consensus Of Linear Multi-Agent Systems Over Signed Directed Graphs

Distributed control of multi-agent systems over nonnegative graphs has attracted significant attention in control community for the past two decades,reaching a relatively mature status.The majority works assume that individuals are always cooperate within a group.As an important part of multi-agent system theory,investigating collective behaviors of multi-agent systems over signed graphs attracts so many researchers' attention all over the word.This thesis investigates sign-consensus problems of general linear multi-agent systems,that is the signs of all agents'states achieve consensus.The interaction between agents is modeled by a signed directed graph,where both cooperation and competition coexist within a group.The graph is allowed to be structurally unbalanced and its adjacency matrix is assumed to be eventually positive.A state feedback control law is proposed to make a group of agents achieve sign-consensus.And some other interesting collective behaviors are discussed over signed graphs by changing the proper control parameters.Distributed control laws are proposed for several classes of graph topologies to make general linear multi-agent systems achieve various kinds of collective behaviors,which include conventional consensus,bipartite sign-consensus,and sign-consensus.For the condition that each individual agent is assumed to access only the local information,a fully distributed control law is proposed.Using this control protocol,we find that sign-consensus can be achieved without requiring the graph to have an eventually positive adjacency matrix.Since the time-varying and switching signed graph is more realistic,this paper studies sign-consensus of linear multi-agent systems over switching signed graphs.Firstly,we consider the signed graph with intermittent communications,which means the underlying graph only needs to be eventually positive for a suitable fraction of each time interval,and in the rest of each time interval,the graph is allowed to have arbitrary topologies.Secondly,we consider the fast switching signed graph.To achieve sign-consensus,condition of the graph topology is obtained,and distributed control law is proposed and analyzed.