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

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.