Continuous time with constraints in general directed networks distributed optimization algorithm design

被引：1

作者：

Yang Z.-Q. ^{[1
]}

Yang X.-W. ^{[2
]}

Chen Z.-Q. ^{[3
]}

机构：

[1] College of Transportation Science and Engineering, Civil Aviation University of China, Tianjin

[2] College of Science, Civil Aviation University of China, Tianjin

[3] College of Artificial Intelligence, Nankai University, Tianjin

来源：

Kongzhi Lilun Yu Yingyong/Control Theory and Applications | 2023年 / 40卷 / 06期

基金：

中国国家自然科学基金;

关键词：

continuous time systems; convex optimization; distributed algorithms; multi-agent systems; unbalanced directed network;

D O I：

10.7641/CTA.2022.20233

中图分类号：

N94 [系统科学]; C94 [];

学科分类号：

0711 ; 081103 ; 1201 ;

摘要：

This paper studies a class of distributed constrained optimization problems on weighted unbalanced directed networks, in which the global objective function is equal to the sum of strongly convex objective functions with the global Lipschitz gradient, and the state of each node is limited to a local constraint set. Each agent only knows its own local objective function and the non-empty constraint set. The goal of this paper is to solve the optimal solution of the problem by using a distributed method. For the optimization problem, a new distributed projection gradient continuous-time coordination algorithm is proposed, in which the imbalance of the graph is eliminated by using the left eigenvector corresponding to the zero eigenvalue of the Laplace matrix. Under some assumptions, combined with the convex analysis theory and Lyapunov stability theory, it is proved that the algorithm can obtain the optimal solution of the problem. Finally, the effectiveness of the algorithm is verified by simulations. © 2023 South China University of Technology. All rights reserved.

引用

页码：1053 / 1060

页数：7

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