A Distributed Algorithm for Solving Linear Algebraic Equations Over Random Networks

• 成果类型: Article
• 署名作者: Alaviani, Seyyed Shaho; Elia, Nicola
• 署名单位: Iowa State University; Clemson University; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3010264
• 发表日期: 2021
• 页码: 2399-2406
• 关键词: Mathematical model; Protocols; Hilbert space; Distributed algorithms; Convex functions; Network topology; TOPOLOGY; Asynchronous; Distributed algorithm; linear algebraic equations; Random graphs

摘要

This article considers the problem of solving linear algebraic equations of the form Ax=b among multiagents, which seek a solution by using local information in presence of random communication topologies. The equation is solved by m agents where each agent only knows a subset of rows of the partitioned matrix [A,b]. The problem is formulated such that this formulation does not need the distribution of random interconnection graphs. Therefore, this framework includes asynchronous updates and/or unreliable communication protocols. The random Krasnoselskii-Mann iterative algorithm is applied that converges almost surely and in mean square to a solution of the problem for any matrices A and b and any initial conditions of agents' states. The algorithm is a totally asynchronous algorithm without requiring a priori B-connectivity and distribution dependency assumptions. The algorithm is able to solve the problem even if the weighted matrix of the graph is periodic and irreducible for synchronous protocol. It is demonstrated that the limit point to which the agents' states converge is determined by the unique solution of a convex optimization problem regardless of the distribution of random communication graphs. Finally, some numerical examples are given to show the results.