{"ID":2885500,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.04020","arxiv_id":"2508.04020","title":"Micro-macro and macro-macro limits for controlled leader-follower systems","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.","short_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 q...","url_abs":"https://arxiv.org/abs/2508.04020","url_pdf":"https://arxiv.org/pdf/2508.04020v1","authors":"[\"Giacomo Albi\",\"Young-Pil Choi\",\"Matteo Piu\",\"Sihyun Song\"]","published":"2025-08-06T02:25:15Z","proceeding":"math.AP","tasks":"[\"math.AP\",\"math.NA\",\"math.OC\"]","methods":"[]","has_code":false}