Lu Wangming, Yu Zhiyong, Chen Zhanheng, Jiang Haijun
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China.
School of Mathematics and Statistics, Yili Normal University, Yining 835000, China.
Math Biosci Eng. 2024 Feb 27;21(3):4440-4462. doi: 10.3934/mbe.2024196.
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.
本文研究了一类具有外部干扰的非线性多智能体系统的预设时间事件触发聚类实际一致性问题。首先，为了达成预设时间聚类实际一致性，引入了一个新的时变函数并设计了一种新颖的分布式连续算法。基于李雅普诺夫稳定性理论和不等式技术，给出了一些充分条件，确保预设时间聚类实际一致性。此外，为避免不同聚类的最终状态重叠，为每个聚类考虑一个虚拟领导者。在这种情况下，进一步建立了一个事件触发分布式协议，并给出了实现预设时间聚类实际一致性的一些相关条件。此外，证明了通过适当选择参数可以避免芝诺行为。最后，给出了一些数值例子以说明理论结果的有效性。
