A Scalable Distributed algorithm for Least Squares Solutions in Double-layered Multi-agent Networks

In this paper, we propose a scalable distributed algorithm for double-layered multi-agent network to cooperatively find the least square solutions to an over-determined linear equation. Compared with existing consensus-based distributed linear equation solvers, the double-layered network structure allows us to implement two types of coordination, namely consensus and conservation, simultaneously. As a result, the proposed algorithm has achieved better scalability in the sense that each agent does not need to know a full row of the overall equation. The convergence of our algorithm is exponential, which has been validated by both analytical proof and numerical simulations.