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

Wangming Lu; Zhiyong Yu; Zhanheng Chen; Haijun Jiang; Wangming Lu; Zhiyong Yu; Zhanheng Chen; Haijun Jiang

doi:10.3934/mbe.2024196

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 3: 4440-4462. doi: 10.3934/mbe.2024196

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Research article

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

1.
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China
2.
School of Mathematics and Statistics, Yili Normal University, Yining 835000, China

Academic Editor: Yang Kuang

Received: 17 December 2023 Revised: 18 January 2024 Accepted: 29 January 2024 Published: 27 February 2024

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.
- event-triggered,
- cluster consensus,
- multi-agent systems,
- prescribed-time
Citation: Wangming Lu, Zhiyong Yu, Zhanheng Chen, Haijun Jiang. Prescribed-time cluster practical consensus for nonlinear multi-agent systems based on event-triggered mechanism[J]. Mathematical Biosciences and Engineering, 2024, 21(3): 4440-4462. doi: 10.3934/mbe.2024196

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Abstract

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.

References

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