Multi-Scale Control of Large Agent Populations: From Density Dynamics to Individual Actuation

[2603.15160] Multi-Scale Control of Large Agent Populations: From Density Dynamics to Individual Actuation Skip to main content Search Submit Donate Log in Electrical Engineering and Systems Science > Systems and Control arXiv:2603.15160 (eess) [Submitted on 16 Mar 2026 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Multi-Scale Control of Large Agent Populations: From Density Dynamics to Individual Actuation Authors: Mario di Bernardo View PDF HTML (experimental) Abstract: We review a body of recent work by the author and collaborators on controlling the spatial organisation of large agent populations across multiple scales. A central theme is the systematic bridging of microscopic agent-level dynamics and macroscopic density descriptions, enabling control design at the most natural level of abstraction and subsequent translation across scales. We show how this multi-scale perspective provides a unified approach to both \emph{direct control}, where every agent is actuated, and \emph{indirect control}, where few leaders or herders steer a larger uncontrolled population. The review covers continuification-based control with robustness under limited sensing and decentralised implementation via distributed density estimation; leader--follower density regulation with dual-feedback stability guarantees and bio-inspired plasticity; optimal-transport methods for coverage control and macro-to-micro discretisation; nonreciprocal field theory for collective decision-making; mean-field control barrier functions for population-level safety; and hierarchical reinforcement learning for settings where closed-form solutions are intractable. Together, these results demonstrate the breadth and versatility of a multi-scale control framework that integrates analytical methods, learning, and physics-inspired approaches for large agent populations. Comments: v2: adds Remark 1 introducing the agent-to-density (A/D) and density-to-agent (D/A) scale-converter terminology; Fig. 1 relabelled; conclusions revised Subjects: Systems and Control (eess.SY) ; Dynamical Systems (math.DS) Cite as: arXiv:2603.15160 [eess.SY] (or arXiv:2603.15160v2 [eess.SY] for this version) https://doi.org/10.48550/arXiv.2603.15160 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mario di Bernardo [ view email ] [v1] Mon, 16 Mar 2026 11:54:18 UTC (33 KB) [v2] Tue, 25 Aug 2026 05:31:15 UTC (34 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: eess.SY < prev | next > new | recent | 2026-03 Change to browse by: cs cs.SY eess math math.DS References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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