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Micro-macro and macro-macro limits for controlled leader-follower systems

Published: August 6, 2025 | arXiv ID: 2508.04020v1

By: Giacomo Albi , Young-Pil Choi , Matteo Piu and more

Potential Business Impact:

Makes many tiny things move together like a team.

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.

Page Count
41 pages

Category
Mathematics:
Analysis of PDEs