Distributed Solvers for Network Linear Equations With Scalarized Compression

• 成果类型: Article
• 署名作者: Wang, Lei; Ren, Zihao; Yuan, Deming; Shi, Guodong
• 署名单位: Zhejiang University; Nanjing University of Science & Technology; University of Sydney
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3488492
• 发表日期: 2025
• 页码: 2644-2651
• 关键词: VECTORS; CONVERGENCE; Signal processing algorithms; Heuristic algorithms; ELECTRONIC MAIL; Consensus algorithm; Communication channels; Distributed algorithms; computational efficiency; australia; compression; consensus; scalar communication; network linear equation

摘要

Distributed computing is fundamental to multiagent systems, with solving distributed linear equations as a typical example. In this article, we study distributed solvers for network linear equations over a network with node-to-node communication messages compressed as scalar values. Our key idea lies in a dimension compression scheme that includes a dimension-compressing vector and a data unfolding step. The compression vector applies to individual node states as an inner product to generate a real-valued message for node communication. In the unfolding step, such scalar message is then plotted along the subspace generated by the compression vector for the local computations. We first present a compressed consensus flow that relies only on such scalarized communication, and show that linear convergence can be achieved with well excited signals for the compression vector. We then employ such a compressed consensus flow as a fundamental consensus subroutine to develop distributed continuous-time and discrete-time solvers for network linear equations, and prove their linear convergence properties under scalar node communications. With scalar communications, a direct benefit would be the reduced node-to-node communication channel burden for distributed computing. Numerical examples are presented to illustrate the effectiveness of the established theoretical results.