Distributed Control Design for Solving Linear Algebraic Equations via Adjustable Domains

• 成果类型: Article
• 署名作者: Li, Juntao; Liang, Cong; Meng, Deyuan
• 署名单位: Henan Normal University; Beihang University; Beihang University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3419185
• 发表日期: 2024
• 页码: 8790-8797
• 关键词: Distributed algorithms; mathematical models; Task analysis; Partitioning algorithms; TOPOLOGY; Symmetric matrices; Matrix decomposition; Adjustable domain; Distributed algorithm; linear algebraic equations (LAEs); multiagent system; time-varying topology

摘要

This article aims to develop a general and designable distributed algorithm for solving linear algebraic equations (LAEs), which departs from the design framework based on orthogonal projection. The concept of adjustable domains for the parameter matrix is introduced, enabling the algorithm to derive flexible and variable updating rules for agents. By leveraging adjustable domains in control design, all agents can exponentially converge to a common (least squares) solution of (un)solvable LAEs under arbitrary initialization conditions, regardless of whether the LAEs admit a unique solution or multiple solutions. Moreover, two novel distributed algorithms for obtaining the least squares solution are proposed within both row and column partitioning frameworks. A simulation example is provided to demonstrate the effectiveness of the proposed distributed algorithms.