Micro-macro and macro-macro limits for controlled leader-follower systems
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866918115803136000 |
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| author | Albi, Giacomo Choi, Young-Pil Piu, Matteo Song, Sihyun |
| author_facet | Albi, Giacomo Choi, Young-Pil Piu, Matteo Song, Sihyun |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04020 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Micro-macro and macro-macro limits for controlled leader-follower systems Albi, Giacomo Choi, Young-Pil Piu, Matteo Song, Sihyun Analysis of PDEs Numerical Analysis Optimization and Control 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. |
| title | Micro-macro and macro-macro limits for controlled leader-follower systems |
| topic | Analysis of PDEs Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2508.04020 |