Event-based Bidirectional Convergence Of Multi-agent Systems

The real-time update of the controller can cause the competition for resources among these agents in the multi-agent systems.In order to improve the utilization of resources,a controller with event-triggered protocol and a time-varying gain are proposed in this paper.Taking the single-integrator multi-agent systems as the staring point,for with-out and with measurement noise,we study the bipartite consensus problem based on event-triggered control protocol,respectively.In the case of no measurement noise,the distributed control protocol based on event triggering is designed for the agents.And the necessary and sufficient conditions for the realization of the bipartite consensus based on the event triggering for the multi-agent systems are proved.We find that the directed sign graph which represents the communication relationship among agents is structure balanced and has a spanning tree,which is the weakest topological condition to ensure that the system achieves the bipartite consensus based on event triggering.Under the condition of measurement noise,with the help of the state transition matrix,Ito formula,Cauchy criterion and algebraic graph theory,we give a necessary and sufficient condi-tion for the system to achieve the mean square bipartite consensus under event-triggered control protocol.