Mathematics > Analysis of PDEs
[Submitted on 6 Aug 2025
]
Title: Micro-macro and macro-macro limits for controlled leader-follower systems
Title: 受控领导者-跟随者系统的微观-宏观和宏观-宏观极限
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.
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