A Double-Layered Framework for Distributed Coordination in Solving Linear Equations
This work addresses the problem of distributed linear equation solving for multi-agent systems, offering reduced per-agent state requirements and flexibility in state dimensions, though it is an incremental improvement over existing consensus-based approaches.
The paper introduces a double-layered multi-agent framework for distributed solution of linear equations, combining consensus and conservation mechanisms. The proposed algorithms require each agent to control only two scalar states and allow heterogeneous state dimensions, outperforming existing consensus-based methods.
This paper proposes a double-layered framework (or form of network) to integrate two mechanisms, termed consensus and conservation, achieving distributed solution of a linear equation. The multi-agent framework considered in the paper is composed of clusters (which serve as a form of aggregating agent) and each cluster consists of a sub-network of agents. By achieving consensus and conservation through agent-agent communications in the same cluster and cluster-cluster communications, distributed algorithms are devised for agents to cooperatively achieve a solution to the overall linear equation. These algorithms outperform existing consensus-based 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.