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Article

A Prescribed-Time Consensus Algorithm for Distributed Time-Varying Optimization Based on Multiagent Systems

1
School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China
2
College of Engineering, Zhejiang Normal University, Jinhua 321004, China
3
College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(13), 2190; https://doi.org/10.3390/math13132190
Submission received: 3 June 2025 / Revised: 30 June 2025 / Accepted: 3 July 2025 / Published: 4 July 2025

Abstract

This paper presents a distributed optimization algorithm for time-varying objective functions utilizing a prescribed-time convergent multi-agent system within undirected communication networks. Departing from conventional time-invariant optimization paradigms with static optimal solutions, our approach specifically addresses the challenge of tracking dynamic optimal trajectories in evolving environments. A novel continuous-time distributed optimization algorithm is developed based on prescribed-time consensus, guaranteeing the consensus attainment among agents within a user-defined timeframe while asymptotically converging to the time-dependent optimal solution. The proposed methodology enables explicit predetermination of convergence duration, representing a significant advancement over existing asymptotic convergence methods. Moreover, two simulation examples on the rendezvous problem and multi-robots control are presented to validate the theoretical results, exhibiting precise time-controlled convergence characteristics and effective tracking performance for time-varying optimization targets.
Keywords: distributed optimization; prescribed-time consensus; time-varying function; multiagent system distributed optimization; prescribed-time consensus; time-varying function; multiagent system

Share and Cite

MDPI and ACS Style

Zheng, Y.; Liu, S.; Zhong, J. A Prescribed-Time Consensus Algorithm for Distributed Time-Varying Optimization Based on Multiagent Systems. Mathematics 2025, 13, 2190. https://doi.org/10.3390/math13132190

AMA Style

Zheng Y, Liu S, Zhong J. A Prescribed-Time Consensus Algorithm for Distributed Time-Varying Optimization Based on Multiagent Systems. Mathematics. 2025; 13(13):2190. https://doi.org/10.3390/math13132190

Chicago/Turabian Style

Zheng, Yanling, Siyu Liu, and Jie Zhong. 2025. "A Prescribed-Time Consensus Algorithm for Distributed Time-Varying Optimization Based on Multiagent Systems" Mathematics 13, no. 13: 2190. https://doi.org/10.3390/math13132190

APA Style

Zheng, Y., Liu, S., & Zhong, J. (2025). A Prescribed-Time Consensus Algorithm for Distributed Time-Varying Optimization Based on Multiagent Systems. Mathematics, 13(13), 2190. https://doi.org/10.3390/math13132190

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