Event-triggered Bipartite Consensus For Discrete-Time Multi-agent Systems

Consensus has always been a hot topic in the research of multi-agent systems.In view of the advantage of event-triggered control in resource utilization,the bipartite consensus problem under event-triggered control for a first-order discrete multi-agent system will be studied in this paper.The main tasks are as follows:In this paper,we first consider the case that the topology of the communication between agents is an undirected connected structurally balanced graph.For each agent,the event-triggered control protocol is designed,including the control input that only depends on the sampling states of itself and its neighbor agents,as well as the event triggering conditions that only depend on its own states,so as to realize the economical utilization of communication resources.Based on graph theory and discrete system stability theory,it is proved that the system can achieve bipartite consensus.At the same time,the range of parameters in the control input and the event triggering conditions is derived to ensure that there is no Zeno phenomenon in the system.Then,the first order discrete agent system under the structurally balanced graph containing the directed spanning tree is further analyzed.Compared with undirected graph,it is more difficult to analyze.In this paper,the event-triggered control input and distributed event triggering conditions are constructed.Based on the stability theory of discrete systems,it is proved that the system achieves bipartite consensus while excluding Zeno phenomenon.Finally,two groups of simulation examples are used to verify the validity of the theoretical results.Finally,for the multi-agent systems under the undirected connected structurally balanced graph and the directed strongly connected structurally balanced graph,the event-triggered control protocol which contains the first-order neighbor information and the second-order neighbor information is designed respectively,and the second-order neighbor information is added to the control input and the event triggering conditions to accelerate the convergence speed of the system.By using Lyapunov stability theory and graph theory,it is proved that the system can realize bipartite consensus and exclude Zeno phenomenon.Finally,a simulation example is used to verify the validity of the theoretical results.