AccScience Publishing / NSCE / Online First / DOI: 10.36922/NSCE025290002
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RESEARCH ARTICLE

Predefined-time practical containment control for multi-agent systems via event-triggered control

Jin-Yue Wang1,2 ,  Xiao-Wen Zhao2* ,  Denghao Pang3 ,  Zhi-Wei Liu4
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1 Songjiang Experimental School Affiliated to SIVA, Shanghai, China
2 School of Mathematics, Hefei University of Technology, Hefei, China
3 School of Internet, Anhui University, Hefei, China
4 School of Automation, Huazhong University of Science and Technology, Wuhan, China
NSCE, 025290002 https://doi.org/10.36922/NSCE025290002
Received: 16 July 2025 | Revised: 9 August 2025 | Accepted: 20 August 2025 | Published online: 3 September 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This paper studies the predefined-time practical containment control (PPCC) problem for multi-agent systems via event-triggered control (ETC). Two ETC protocols are proposed based on time-varying functions. Both controllers guarantee that PPCC is achieved, where the state converges to an adjustable neighborhood of the common state, meeting the requirements of practical applications. The designed time-varying gain is bounded, preventing the occurrence of the Zeno phenomenon at a predefined time. To overcome the chattering phenomenon of the sign function during discontinuous differentiation, a saturation function is introduced instead. An improved ETC protocol is then designed. Finally, we prove that the Zeno phenomenon can be avoided at any moment and verify the effectiveness of the control method by numerical results.

Keywords
Event-triggered control
Multi-agent systems
Predefined-time containment control
Funding
This work was supported by the National Natural Science Foundation of China under Grant 62573173, 62173121 and 12301185.
Conflict of interest
Xiao-Wen Zhao is an Associate Editor and Zhi-Wei Liu is an Editorial Board Member of this journal, but were not in any way involved in the editorial and peer-review process conducted for this paper, directly or indirectly. Separately, other authors declared that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.
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