Prescribed-time cluster practical consensus for nonlinear multi-agent systems based on event-triggered mechanism.

This paper investigates the prescribed-time event-triggered cluster practical consensus problem for a class of nonlinear multi-agent systems with external disturbances. To begin, to reach the prescribed-time cluster practical consensus, a new time-varying function is introduced and a novel distributed continuous algorithm is designed. Based on the Lyapunov stability theory and inequality techniques, some sufficient conditions are given, ensuring the prescribed-time cluster practical consensus. Moreover, to avoid different clusters' final states overlapping, a virtual leader is considered for each cluster. In this case, an event-triggered distributed protocol is further established and some related conditions are given for achieving prescribed-time cluster practical consensus. Additionally, it is proven that the Zeno behavior can be avioded by choosing parameters appropriately. Finally, some numerical examples are presented to show the effectiveness of the theoretical results.