Multi-Scale Control of Large Agent Populations: From Density Dynamics to Individual Actuation
This work addresses the problem of controlling spatial organization in large agent populations for applications like robotics and swarm systems, presenting a comprehensive review that integrates analytical and learning-based approaches, but it is incremental as it synthesizes existing methods rather than introducing a new paradigm.
The paper reviews a multi-scale control framework for managing large agent populations by bridging microscopic agent dynamics and macroscopic density descriptions, enabling both direct and indirect control strategies. It demonstrates the framework's versatility through various methods, including continuification-based control, leader-follower regulation, optimal transport, and hierarchical reinforcement learning, though specific numerical results are not provided.
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.