Scalable, Distributed Algorithms for Solving Linear Equations via Double-Layered Networks
Scalable, Distributed Algorithms for Solving Linear Equations via Double-Layered Networks
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DOI：
10.1109/tac.2019.2919101
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发表时间：
2020-03
影响因子：
6.8
通讯作者：
Xuan Wang;Shaoshuai Mou;B. Anderson
中科院分区：
文献类型：
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作者：
Xuan Wang;Shaoshuai Mou;B. Anderson
本文提出了可扩展的，分布式算法求解线性方程组，通过整合两种机制，称为共识和保护，在双层多智能体网络。本文所考虑的多智能体网络是由簇组成的，每个簇由一个聚集器和一个智能体子网组成。通过实现共识和守恒，通过在同一集群和聚合器之间的聚合器，聚合器通信，分别在不同的集群，分布式算法设计的代理合作实现整体线性方程的解决方案。这些算法优于现有算法，包括但不限于以下方面-第一，每个代理不必知道整个方程的完整行或列那么多;第二，当集群数量和代理数量足够大时，每个代理仅需要控制少至两个标量状态;第三，在所提出的算法中，代理状态的维度不必相同（而相反，基于标准一致性思想的算法本质上要求所有代理的状态具有相同的维度）。分析证明和仿真结果都验证了所提出的分布式算法在求解线性方程组时的指数收敛性。
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–agent communications in the same cluster and aggregator–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—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’ 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’ 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.