{"paper":{"title":"Benamou-Brenier Formulation of Optimal Transport for Nonlinear Control Systems on Rd","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Karthik Elamvazhuthi","submitted_at":"2024-07-22T23:14:38Z","abstract_excerpt":"In this paper we consider the Benamou-Brenier formulation of optimal transport for nonlinear control affine systems on $\\Rd$, removing the compactness assumption of the underlying manifold in previous work by the author. By using Bernard's Young measure based weak formulation of optimal transport, the results are established for cases not covered by previous treatments using the Monge problem. Particularly, no assumptions are made on the non-existence of singular minimizing controls or the cost function being Lipschitz. Therefore, the existence of solutions to dynamical formulation is establis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.16088","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.16088/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}