A Distributed Least-Squares Solver for Linear Systems of Algebraic Equations

This paper introduces a consensus-based continuous-time distributed algorithm to find the least-squares solution to overdetermined systems of linear algebraic equations over directed multi-agent networks. It is assumed that each agent has only access to a subsystem of the algebraic equations, and the underlying communication network is strongly connected. We show that, along the flow of the proposed algorithm, the local estimate of each agent converges exponentially to the exact least-squares solution, provided that the aggregate system of linear equations has full column rank, and each agent knows an upper bound on the total number of the participating agents in the network. Copyright (C) 2022 The Authors.