Faster Consensus via a Sparser Controller

TL;DR

This paper explores the design of an optimal, sparsely connected controller that accelerates consensus in multi-agent systems with delayed feedback, highlighting the benefits of reduced communication links.

Contribution

It introduces a novel optimal control architecture that maximizes convergence speed by leveraging sparsity under communication delays.

Findings

Optimal controller is sparsely connected.

Sparsity improves convergence speed.

Delays influence controller architecture.

Abstract

In this paper, we investigate the architecture of an optimal controller that maximizes the convergence speed of a consensus protocol with single-integrator dynamics. Under the assumption that communication delays increase with the number of hops from which information is allowed to reach each agent, we address the optimal control design under delayed feedback and show that the optimal controller features, in general, a sparsely connected architecture.