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Micro-macro and macro-macro limits for controlled leader-follower systems
arXiv cs.NA0 views
arXiv:2508.04020v2 Announce Type: replace-cross 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.
Source:https://arxiv.org/abs/2508.04020PreviousProvably convergent stochastic fixed-point algorithm for free-support Wasserstein barycenter of continuous non-parametric measuresNextAn Alternating Direction Method of Multipliers for Topology Optimization
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