Fixed-time cluster consensus for multi-agent systems via event-triggered control.

This paper focuses on the fixed-time (FXT) cluster consensus of multi-agent systems (MASs) with nonlinear dynamics and uncertain disturbances, in which the network topology contains both cooperative and competitive relationships. First, a novel static event-triggered control protocol with separate information exchange rules for intra-cluster and inter-cluster agents is devised, which can effectively balance the influence of intra and inter groups information well by adjusting their gain weights. By using graph theory and Lyapunov stability theory, some sufficient conditions are obtained to ensure the FXT cluster consensus. Second, to optimize control costs and reduce the frequency of event-triggered, a distributed dynamic event-triggered control protocol is designed. Furthermore, according to event-triggered mechanisms and inequalities, the Zeno phenomenon can be excluded under these two control protocols. Finally, the validity of the proposed protocols is verified by two numerical examples.