Consensus Over Signed Digraphs With Communication Constraints

With the recent technological advance on communication resources,distributed control of multi-agent systems has been studied more and more widely.Some significant results,such as consensus,formation control,and synchronization,have attracted attention of plentiful experts from diverse disciplines.Specially,the consensus of the multi-agent system is a focal research topic and has been intensively investigated in the past decade.This paper studies the consensus problem in networks of agents with antagonistic interactions and communication delays.The main work of this paper is listed as follows:The first chapter summarizes the current research status and prospects of multi-agent networks.Then,we analyse some consensus and distributed control of recent research results.Furthermore,we present the motivation and derivation of our main works in this paper.The second chapter investigates the consensus problem in networks of agents with antagonistic interactions and communication delays.For undirected signed networks,we respectively establish two dynamic models corresponding to linear and nonlinear coupling.Based on stability theory and related graph theory,it is proved that all agents on signed networks can reach agreement on a consensus value except for the sign when the associated signed graph is connected.Further,a bipartite consensus solution is given for linear coupling networks,and an explicit expression associating with bipartite consensus solution is provided for nonlinear coupling networks.Finally,numerical simulations are given to demonstrate the effectiveness of our proposed results.The third chapter solves consensus problems over signed digraphs with arbitrary finite commu-nication delays.For the considered system,the information flow is directed and only locally delayed information can be used for each node.Following Lyapunov's theorem and Barbalat's lemma,we find that bipartite consensus of this system can be realized when the associated signed digraph is strongly connected.Furthermore,for structurally balanced networks,this paper studies the pinning partite consensus for the considered system.we design a pinning scheme to pin any one agent in the signed network,and obtain that the network achieve pinning bipartite consensus with any initial conditions.Finally,two examples axe provided to demonstrate the effectiveness of our main results.Finally,the forth chapter summarizes the main results and contributions of this dissertation.Some possible future work about this issue are introduced.