Event-triggered Bipartite Consensus for Multi-agent Systems Associated with Signed Graphs

To reduce the unnecessary waste of limited resources, such as network bandwidth, communication cost, and the energy of the agent itself, the event-triggered problem of bipartite consensus for multi-agent systems with first order under the undirected signed graph topology is studied. On the basis of the properties of the connected signed graph, a novel bipartite consensus protocol with the coexistence of cooperative and competitive interactions is designed, which makes the interested states of each agent reach a consensus with identical magnitude but opposite sign. Furthermore, using the algebraic graph and matrix theories, the appropriate conditions for multi-agent systems to achieve bipartite consensus are obtained and the final agreement of each agent is achieved. In the study of bipartite consensus, the typical control method assumes periodic sampling control, which will cause problems, such as increased energy consumption and high bandwidth occupation. Event-triggered control is introduced, that is, an event-triggered function is constructed. When an agent state measurement error satisfies the function, the agent triggers an event. Then, all agents trigger the event and update the control input. Continuous communication between agents is not required, which reduces energy consumption and improves resource utilization. Finally, simulations are conducted to illustrate the efficiency of the theoretical results of the proposed method.