Projective Group Consensus Of Multi-agent Systems In Networks

Since the 20 th century,because of its wide application and potential social value in many fields such as intelligent robot,satellite communication network and unmanned aerial,multi-agent system has gradually attracted the attention and interest of researchers from different subject areas.Consensus problem as one of the most basic problems in coordinated control of multi-agent systems,plays a vital role in the field of control theory.With the development of society and the expansion of people's demand for application systems,the complexity of research system model is increasing.The traditional single equilibrium point in multi-agent systems that cannot meet the application control demand of the system,as a consequence,more and more people focuses on group consensus.However,in the existing researches on group consensus,the relationship between the convergence states of systems in different groups is often unknown or uncertain.In recent years,some scholars have proposed a special kind of group consensus,namely bipartite consensus.Most of the literatures about bipartite consensus have required some conditions such as the balance of signed network graph,which limits the application of multi-agent system in practical background to some extent.Based on previous work,this paper analyzes the projective group consensus of multi-agent system under network environment.The main contents are as follows:(1)This paper proposes projective group consensus of second order multi-agent systems under the directed topological structure.We have designed a novel distributed control protocol.Based on the Lyapunov stability theory,algebraic graph theory,and some necessary matrix theory,sufficient conditions for delay-free and delay cases are derived.Furthermore,conditions of signed graph are not necessary structurally balanced in theory.(2)During the projective consensus problem of multi-agent systems under the cluster structure,a new leader called smart leader is introduced for the possible actuator faults.We construct a control algorithm for the leader,which can be freely converted.By using the stability theory of switching systems,we derive some sufficient conditions to achieve the projective consensus of the systems.In addition,based on the Laplace transform property,the system can ensure the tracking error to be bounded when actuator faults occur on some of followers.(3)The concept of projective group consensus with different scaling factors for second-order multi-agent systems is proposed.Then the problem of linear projective consensus for second order multi-agent system with directed network topology is discussed in this paper.By designing an effective control protocol and using algebraic graph theory and stability theory,the sufficient and necessary conditions for linear projective consensus of second-order multi-agent system with and without communication delay are derived.In addition,numerical examples are provided to illustrate the validity of the obtained result.