Fully distributed constrained optimization algorithm over unbalanced network and its application to smart grids

IF 2.5 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2025-08-16 DOI:10.1016/j.sysconle.2025.106211

Xiasheng Shi , Lei Xu

{"title":"Fully distributed constrained optimization algorithm over unbalanced network and its application to smart grids","authors":"Xiasheng Shi , Lei Xu","doi":"10.1016/j.sysconle.2025.106211","DOIUrl":null,"url":null,"abstract":"<div><div>In practical engineering, due to the limited bandwidth and other physical constraints, directed network communication topology among agents is more common. This paper studies the distributed constrained optimization problem over the weight-unbalanced directed network, considering local inequality and coupled equality constraints. First, a distributed consensus scheme with a time-based generator is provided to estimate the left eigenvector of the Laplacian matrix. Building on this estimator, an adaptive proportional–integral-based gradient flow scheme is designed to solve the coupled constraint, introducing a time-varying control parameter to remove the requirement of the Laplacian matrix’s eigenvalues. Subsequently, a fully distributed primal–dual optimization method is proposed based on KKT conditions for the constrained optimization problem with a nonsmooth objective function. The optimality and convergence analysis are conducted through Lyapunov theory under the strongly connected and weight-unbalanced directed network. Finally, the established method is applied to the economic dispatch problem in smart grids.</div></div>","PeriodicalId":49450,"journal":{"name":"Systems & Control Letters","volume":"204 ","pages":"Article 106211"},"PeriodicalIF":2.5000,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Systems & Control Letters","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167691125001938","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}

引用次数: 0

Abstract

In practical engineering, due to the limited bandwidth and other physical constraints, directed network communication topology among agents is more common. This paper studies the distributed constrained optimization problem over the weight-unbalanced directed network, considering local inequality and coupled equality constraints. First, a distributed consensus scheme with a time-based generator is provided to estimate the left eigenvector of the Laplacian matrix. Building on this estimator, an adaptive proportional–integral-based gradient flow scheme is designed to solve the coupled constraint, introducing a time-varying control parameter to remove the requirement of the Laplacian matrix’s eigenvalues. Subsequently, a fully distributed primal–dual optimization method is proposed based on KKT conditions for the constrained optimization problem with a nonsmooth objective function. The optimality and convergence analysis are conducted through Lyapunov theory under the strongly connected and weight-unbalanced directed network. Finally, the established method is applied to the economic dispatch problem in smart grids.

查看原文本刊更多论文

不平衡网络的全分布约束优化算法及其在智能电网中的应用

在实际工程中，由于有限的带宽和其他物理约束，代理之间的定向网络通信拓扑更为常见。研究了考虑局部不等式和耦合等式约束的权重不平衡有向网络的分布式约束优化问题。首先，提出了一种基于时间生成器的分布式一致性方案来估计拉普拉斯矩阵的左特征向量。在此基础上，设计了一种基于比例积分的自适应梯度流方案来解决耦合约束，引入时变控制参数来消除对拉普拉斯矩阵特征值的要求。随后，针对具有非光滑目标函数的约束优化问题，提出了一种基于KKT条件的全分布原对偶优化方法。利用Lyapunov理论对强连通权不平衡有向网络进行了最优性和收敛性分析。最后，将所建立的方法应用于智能电网的经济调度问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Systems & Control Letters 工程技术-运筹学与管理科学

CiteScore

4.60

自引率

3.80%

发文量

144

审稿时长

6 months

期刊介绍： Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.