Solving Linear Equations With Separable Problem Data Over Directed Networks

作     者：Srivastava, Priyank Cortes, Jorge 

作者机构：Univ Calif San Diego Dept Mech & Aerosp Engn San Diego CA 92122 USA 

出 版 物：《IEEE CONTROL SYSTEMS LETTERS》 (IEEE Control Syst. Lett.)

年 卷 期：2022年第6卷

页      面：596-601页

核心收录：

基　　金：NSF [1917177, 1947050] Div Of Electrical, Commun & Cyber Sys Directorate For Engineering Funding Source: National Science Foundation 

主　　题：Heuristic algorithms Distributed algorithms Optimization Mathematical model Eigenvalues and eigenfunctions Manganese Symmetric matrices Linear algebraic equations distributed algorithms directed graphs 

摘      要：This letter deals with linear algebraic equations where the global coefficient matrix and constant vector are given respectively, by the summation of the coefficient matrices and constant vectors of the individual agents. Our approach is based on reformulating the original problem as an unconstrained optimization. Based on this exact reformulation, we first provide a gradient-based, centralized algorithm which serves as a reference for the ensuing design of distributed algorithms. We propose two sets of exponentially stable continuous-time distributed algorithms that do not require the individual agent matrices to be invertible, and are based on estimating non-distributed terms in the centralized algorithm using dynamic average consensus. The first algorithm works for time-varying weight-balanced directed networks, and the second algorithm works for general directed networks for which the communication graphs might not be balanced. Numerical simulations illustrate our results.