Control of agent-based models across scales

This thesis presents a comprehensive investigation into modeling and controlling high dimensional agent-based models within a multi-scale framework. At the core of this research lies the fundamental challenge of overcoming computational bottlenecks in solving optimal control problems with many-agent dynamics. Solutions to this class of optimization problems are doubly cursed by the dimensionality of the system, first in the number of interacting agents, and second in the dimensionality of each agent’s underlying dynamics. This dual nature suggests a broad spectrum of techniques to enhance the efficiency and scalability of optimal control computations across various modeling resolutions. At the microscopic scale, we address this double trouble at the agent-to-agent interaction level through data-driven approximation techniques. We combine neural network approximation models with control theory and existing solvers for synthetic data generation, resulting in efficient and effective control laws. When the computational challenge is mostly linked to a large number of agents, we switch to a macroscopic viewpoint, formulating an optimal control problem for the distribution of agents evolving in the underlying physical space. The resulting mean field dynamics offer an ideal framework to analyze emergent behaviors of many-agent systems and addressing PDE-constrained optimization problems to stabilize the system around desired steady states. When both the number of agents and the dimensionality of their underlying dynamics make traditional control synthesis impractical, we introduce a mesoscopic kinetic approximation framework that models agent densities as plasma-like matter. The mean-field behavior is approximated by averaging over controlled subsystems of interacting agent pairs in a Monte Carlo fashion. The accuracy of this approximation relies on high-frequency sampling of controlled binary interactions, for which we leverage neural network speed-ups similar to those used at the microscopic scale.