{"paper":{"title":"Optimality conditions and regularity results for time optimal control problems with differential inclusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Antonio Marigonda, Khai T. Nguyen, Piermarco Cannarsa","submitted_at":"2013-11-18T14:58:29Z","abstract_excerpt":"We study the time optimal control problem with a general target $\\mathcal S$ for a class of differential inclusions that satisfy mild smoothness and controllability assumptions. In particular, we do not require Petrov's condition at the boundary of $\\mathcal S$. Consequently, the minimum time function $T(\\cdot)$ fails to be locally Lipschitz---never mind semiconcave---near $\\mathcal S$. Instead of such a regularity, we use an exterior sphere condition for the hypograph of $T(\\cdot)$ to develop the analysis. In this way, we obtain dual arc inclusions which we apply to show the constancy of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4415","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}