English

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.

Keywords

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

R2 v1 2026-07-01T04:36:25.959Z