A Specified-Time Convergent Multiagent System for Distributed Optimization With a Time-Varying Objective Function

• Published in: IEEE transactions on automatic control Vol. 69; no. 2; pp. 1257 - 1264
• Main Authors: Zheng, Yanling, Liu, Qingshan, Wang, Jun
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.02.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Convergence; Decentralized control; Distributed optimization; Linear programming; Multi-agent systems; multiagent system; Multiagent systems; Optimization; Protocols; Settling; specified-time convergence; Time dependence; time-varying objective function; Time-varying systems; Upper bound; Upper bounds
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2023.3282065

This technical note presents a specified-time convergent multiagent system for distributed optimization with a time-varying objective function subject to equality constraints. Different from the static optimal solutions to most existing distributed optimization problems, the optimal solutions are time varying due to the time-varying objective function in this problem. A distributed protocol law is designed to ensure all the agents' convergence to feasible and suboptimal solutions within a specified settling time and keep tracking the time-dependent optimal solutions. The specified-time convergence of the system and the asymptotic optimality of the solution generated by the system are proved based on the Lyapunov theory. A salient feature of the multiagent system is that its upper bound of settling time can be specified in advance. Two examples are presented to illustrate the theoretical results.