Micro-macro and macro-macro limits for controlled leader-follower systems
Analysis of PDEs
2025-08-07 v1 Numerical Analysis
Numerical Analysis
Optimization and Control
Abstract
We study a leader-follower system of interacting particles subject to feedback control and derive its mean-field limits through a two-step passage: first to a micro-macro system coupling leader particles with a follower fluid, and then to a fully continuum macro-macro system. For each limiting procedure, we establish quantitative stability and convergence estimates based on modulated energy methods and Wasserstein distances. These results provide a rigorous foundation for the hierarchical reduction of controlled multi-agent systems. Numerical simulations are presented, including examples with interaction potentials beyond the analytical class considered, to demonstrate the dynamics and support the theoretical results.
Cite
@article{arxiv.2508.04020,
title = {Micro-macro and macro-macro limits for controlled leader-follower systems},
author = {Giacomo Albi and Young-Pil Choi and Matteo Piu and Sihyun Song},
journal= {arXiv preprint arXiv:2508.04020},
year = {2025}
}
Comments
41 pages, 6 figures