Scalable, Distributed Algorithms for Solving Linear Equations via Double-Layered Networks

摘要

This paper proposes scalable, distributed algorithms for solving linear equations by integrating two mechanisms, termed consensus and conservation, in double-layered multiagent networks. The multiagent network considered in this paper is composed of clusters and each cluster consists of an aggregator and a subnetwork of agents. By achieving consensus and conservation through agent & x2013;agent communications in the same cluster and aggregator & x2013;aggregator communications among different clusters, respectively, distributed algorithms are devised for agents to cooperatively achieve a solution to the overall linear equation. These algorithms outperform existing algorithms, including but not limited to the following aspects & x2014;first, each agent does not have to know as much as a complete row or column of the overall equation; second, each agent only needs to control as few as two scalar states when the number of clusters and the number of agents are sufficiently large; third, the dimensions of agents & x2019; states in the proposed algorithms do not have to be the same (while in contrast, algorithms based on the idea of standard consensus inherently require all agents & x2019; states to be of the same dimension). Both analytical proof and simulation results are provided to validate exponential convergence of the proposed distributed algorithms in solving linear equations.