A Distributed Algorithm with Scalar States for Solving Linear Equations

Abstract

Based on a combination of consensus and conservation, the paper develops a distributed update for solving linear equations by multi-agent networks, in which each agent only knows just a small part of the overall equation and can only communicate with its nearby neighbors. In the proposed distributed update, each agent knows only two scalar entries of the defining matrix of the overall equation and controls just two scalar states. Given the underlying networks to be connected and undirected, the proposed distributed update enables agents to collaboratively achieve a solution to the overall equation. Analytical proof is provided for the exponential convergence of the proposed update, which is also validated by numerical simulations. Show more