Stabilization via localized controls in nonlocal models of crowd dynamics
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917605804081152 |
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| author | Pogodaev, Nikolay Rossi, Francesco |
| author_facet | Pogodaev, Nikolay Rossi, Francesco |
| contents | We consider a control system driven by a nonlocal continuity equation. Admissible controls are Lipschitz vector fields acting inside a fixed open set. We demonstrate that small perturbations of the initial measure, traced along Wasserstein geodesics, may be neutralized by admissible controls. More specifically, initial perturbations of order $\varepsilon$ can be reduced to order $\varepsilon^{1+κ}$, where $κ$ is a positive constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03580 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stabilization via localized controls in nonlocal models of crowd dynamics Pogodaev, Nikolay Rossi, Francesco Optimization and Control 93C20, 93D20, 35Q93 We consider a control system driven by a nonlocal continuity equation. Admissible controls are Lipschitz vector fields acting inside a fixed open set. We demonstrate that small perturbations of the initial measure, traced along Wasserstein geodesics, may be neutralized by admissible controls. More specifically, initial perturbations of order $\varepsilon$ can be reduced to order $\varepsilon^{1+κ}$, where $κ$ is a positive constant. |
| title | Stabilization via localized controls in nonlocal models of crowd dynamics |
| topic | Optimization and Control 93C20, 93D20, 35Q93 |
| url | https://arxiv.org/abs/2403.03580 |