Event-triggered Bipartite Consensus for Multi-agent Systems with Antagonistic Interactions

This paper investigates event-triggered control for first-order multi-agent systems with structurally balanced signed graphs. A distributed continuous event-triggered consensus mechanism is firstly proposed for each agent, including the control law based on local sampled states, and the triggering condition constructed with its own state, the sampled states of itself and its neighbours, and an extra signal. No knowledge of the global network is needed. By applying Lyapunov stability theory and the algebraic graph theory, we prove that all agents can reach agreement with identical magnitude but opposite sign while Zeno behaviour is excluded. Moreover, the periodic implementation of the event-triggered consensus algorithm is proposed. The criteria of co-designing the triggering condition parameter and the verification period is established to guarantee the bipartite consensus of the systems. Finally, simulations, including a numerical example and a group of multiple mobile robots, are shown to illustrate the efficiency of the proposed theoretical results.