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

We study the problem of finding the least-squares solution to the time-varying linear algebraic equation, z(t) = H(t)y(t), over an undirected network in a distributed manner. Each agent ihas access to a time-varying row rector, hi
^T
(t)of H(t)as well as the corresponding entry zi(t)in 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.