On Distributed Control of Continuum Swarms: Local Controllers as Differential Operators

Fuente: arXiv
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Main Authors: Emerick, Max, Chhatoi, Saroj Prasad, Bamieh, Bassam
Format: Preprint
Published: 2026
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author Emerick, Max
Chhatoi, Saroj Prasad
Bamieh, Bassam
author_facet Emerick, Max
Chhatoi, Saroj Prasad
Bamieh, Bassam
contents We study the problem of distributed control of large-scale robotic swarms which can be modeled as continuum densities evolving under the continuity equation. We propose a formalization of distributed controllers as (generally nonlinear) differential operators, in which control inputs depend only on local information about the state and environment. This perspective yields a fully local, PDE-based framework for analysis and design. We apply this framework to the problem of stabilizing a swarm density around an arbitrary target density, and investigate fundamental limitations of low-order distributed controllers in achieving this goal. In particular, we show that controllers which act in a purely pointwise manner are incompatible with natural system symmetries and strong forms of stability, and must rely on mixing-type behavior to achieve stabilization. In contrast, we present a simple first-order control law which achieves stabilization and enjoys substantially stronger properties.
format Preprint
id arxiv_https___arxiv_org_abs_2604_25187
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On Distributed Control of Continuum Swarms: Local Controllers as Differential Operators
Emerick, Max
Chhatoi, Saroj Prasad
Bamieh, Bassam
Systems and Control
93C20 (Primary), 93A14, 35Q49 (Secondary)
We study the problem of distributed control of large-scale robotic swarms which can be modeled as continuum densities evolving under the continuity equation. We propose a formalization of distributed controllers as (generally nonlinear) differential operators, in which control inputs depend only on local information about the state and environment. This perspective yields a fully local, PDE-based framework for analysis and design. We apply this framework to the problem of stabilizing a swarm density around an arbitrary target density, and investigate fundamental limitations of low-order distributed controllers in achieving this goal. In particular, we show that controllers which act in a purely pointwise manner are incompatible with natural system symmetries and strong forms of stability, and must rely on mixing-type behavior to achieve stabilization. In contrast, we present a simple first-order control law which achieves stabilization and enjoys substantially stronger properties.
title On Distributed Control of Continuum Swarms: Local Controllers as Differential Operators
topic Systems and Control
93C20 (Primary), 93A14, 35Q49 (Secondary)
url https://arxiv.org/abs/2604.25187