In this paper, 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.
Micro-macro and macro-macro limits for controlled leader-follower systems
Albi, Giacomo
;Piu, Matteo;
2026-01-01
Abstract
In this paper, 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.
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