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.

中文翻译：

---

通过双层网络求解线性方程的可扩展分布式算法


本文提出了可扩展的分布式算法，通过在双层多智能体网络中集成两种机制（称为共识和守恒）来求解线性方程。本文考虑的多智能体网络由集群组成，每个集群由一个聚合器和一个智能体子网络组成。通过分别通过同一集群中的智能体与智能体之间的通信以及不同集群之间的聚合器与聚合器之间的通信来实现共识和守恒，设计了分布式算法，使智能体能够协作地求解整个线性方程。这些算法优于现有算法，包括但不限于以下几个方面：首先，每个智能体不必了解整个方程的完整行或列；其次，当簇数和智能体数量足够大时，每个智能体只需要控制最少两个标量状态；第三，所提出的算法中代理状态的维度不必相同（相反，基于标准共识思想的算法本质上要求所有代理状态具有相同的维度）。提供了分析证明和仿真结果来验证所提出的分布式算法在求解线性方程时的指数收敛性。