Fast Distributed Least-Squares Solver for Linear Time-Varying Equations

Abstract

We study the problem of finding the least-squares solution to the time-varying linear algebraic equation, $\mathbf{z}(t)= \mathbf{H}(t)\mathbf{y}(t)$ , over an undirected network in a distributed manner. Each agent $i$ has access to a time-varying row rector, $\mathbf{h}_{i}^{\top}(t)$ of $\mathbf{H}(t)$ as well as the corresponding entry $z_{i}(t)$ in $\mathbf{z}(t)$ . The goal is to find the least-squares solution by communicating with neighbors over an undirected interaction graph. We propose a robust dynamic average-consensus algorithm, which allows the agents to precisely estimate the time-varying average signals needed to calculate the least-squares solution in a distributed manner. Since the estimation error corresponding to the presented dynamic average-consensus algorithm converges to zero in finite time, the proposed distributed algorithm yields the least-squares solution in finite time. Numerical simulations are provided to illustrate the effectiveness of the proposed algorithm.