On Distributed Control of Continuum Swarms: Local Controllers as Differential Operators
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915970126184448 |
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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 |
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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 |