Transport maps as flows of control-affine systems
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912440590008320 |
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| author | Caponigro, Marco Vicari, Arianna |
| author_facet | Caponigro, Marco Vicari, Arianna |
| contents | We consider the problem of transporting \nota{one probability measure into another through} the flow of a given driftless control-affine system. Under suitable regularity conditions, the controllability of the system by means of open-loop controls is a sufficient condition for the existence of time-varying feedback controls such that the $1$-time flow of the system is the optimal transport map for the quadratic cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12793 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transport maps as flows of control-affine systems Caponigro, Marco Vicari, Arianna Optimization and Control 93B05 93B05 93B05, 35Q49 We consider the problem of transporting \nota{one probability measure into another through} the flow of a given driftless control-affine system. Under suitable regularity conditions, the controllability of the system by means of open-loop controls is a sufficient condition for the existence of time-varying feedback controls such that the $1$-time flow of the system is the optimal transport map for the quadratic cost. |
| title | Transport maps as flows of control-affine systems |
| topic | Optimization and Control 93B05 93B05 93B05, 35Q49 |
| url | https://arxiv.org/abs/2404.12793 |