Robust Macroscopic Density Control of Heterogeneous Multi-Agent Systems

TL;DR

This paper introduces a scalable control framework for large heterogeneous multi-agent systems, ensuring robust density regulation despite disturbances and unmodeled dynamics, with proven exponential convergence.

Contribution

It develops a novel macroscopic density control method directly at the PDE level, handling heterogeneity and uncertainties with guaranteed convergence.

Findings

Proven exponential convergence in density control.

Robustness to unmodeled dynamics and environmental disturbances.

Validated through numerical experiments on diverse systems.

Abstract

Modern applications, such as orchestrating the collective behavior of robotic swarms or traffic flows, require the coordination of large groups of agents evolving in unstructured environments, where disturbances and unmodeled dynamics are unavoidable. In this work, we develop a scalable macroscopic density control framework in which a feedback law is designed directly at the level of an advection--diffusion partial differential equation. We formulate the control problem in the density space and prove global exponential convergence towards the desired behavior in $\mathcal{L}^2$ with guaranteed asymptotic rejection of bounded unknown drift terms, explicitly accounting for heterogeneous agent dynamics, unmodeled behaviors, and environmental perturbations. Our theoretical findings are corroborated by numerical experiments spanning heterogeneous oscillators, traffic systems, and swarm robotics in partially unknown environments.