k-Dimensional Agreement in Multiagent Systems

TL;DR

This paper introduces a distributed algorithm for multiagent systems that computes multiple weighted means simultaneously, leveraging linear protocols to achieve agreement on a k-dimensional space efficiently.

Contribution

It presents a novel approach to multi-dimensional agreement, enabling simultaneous consensus on multiple functions with reduced complexity compared to traditional methods.

Findings

Linear algorithms can compute oblique projections of initial conditions.

Protocols can be tailored to specific communication graphs.

Single algorithms can solve multiple consensus problems efficiently.

Abstract

Given a network of agents, we study the problem of designing a distributed algorithm that computes k independent weighted means of the network's initial conditions (namely, the agents agree on a k-dimensional space). Akin to average consensus, this problem finds applications in distributed computing and sensing, where agents seek to simultaneously evaluate k independent functions at a common point by running a single coordination algorithm. We show that linear algorithms can agree on quantities that are oblique projections of the vector of initial conditions, and we provide techniques to design protocols that are compatible with a pre-specified communication graph. More broadly, our results show that a single agreement algorithm can solve $k$ consensus problems simultaneously at a fraction of the complexity of classical approaches but, in general, it requires higher network connectivity.