Fixed-Time Bipartite Consensus Of Multi-Agent Systems Using Event-Triggered Machanism

In recent years,cooperative control has been widely applied in many different fields and disciplines,such as smart power grid,unmanned vehicle,satellite attitude control and multi-sensor system,etc.As the core issue in the field of collaborative control,consensus has always been the focus of scholars.On the basis of the existing research work,using algebraic graph theory,matrix theory,Lyapunov stability theory and distributed correlation theory,this paper discusses bipartite consensus and average bipartite consensus of multi-agent system under fixed time.The main research work of this paper is introduced as follows:Firstly,the problem of fixed-time bipartite consensus for first-order integrator multi-agent systems under signed graph is studied.In this paper,two new distributed control strategies based on static event-triggered mechanism are proposed.For each agent,the event-triggered condition based on state information is given.When the state error meets the specific conditions,the data update and information transmission are carried out once,which can effectively relieve the communication pressure of the system,reduce the update frequency of the controller,and eliminate Zeno behavior.Compared with the finite-time consensus control strategy,the fixed time consensus control strategy solves the problem of uncertain convergence time caused by the random change of the initial state of the system.Secondly,on the basis of static event-triggered strategy,two distributed event-triggered control strategies based on dynamic event-triggered mechanism are proposed to achieve bipartite consensus and average bipartite consensus in fixed time for multi-agent system.In this strategy,a dynamic variable related to the system state is designed as the threshold of event triggering,which gradually converges as the system state converges.In this way,the system can reduce unnecessary events,better balance system performance and the number of event triggering,and eliminate Zeno behavior.Finally,the fixed-time bipartite consensus problem of the leader-following multi-agent system under the directed signed graph is studied.First,by combining the event-triggered mechanism and fixed-time control,a bipartite fixed-time event-triggered observer is proposed to estimate the leader's state,which can accurately estimate the leader's state only through discontinuous communication.Furthermore,a fixed-time controller based on the bipartite fixed-time event-triggered observer is constructed,so that the multi-agent system can reach bipartite consensus in a fixed time.