{"paper":{"title":"A note on systems with ordinary and impulsive controls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.OC","authors_text":"Franco Rampazzo, M. Soledad Aronna","submitted_at":"2013-12-30T14:25:02Z","abstract_excerpt":"We investigate an everywhere defined notion of solution for control systems whose dynamics depend nonlinearly on the control $u$ and state $x,$ and are affine in the time derivative $\\dot u.$ For this reason, the input $u,$ which is allowed to be Lebesgue integrable, is called impulsive, while a second, bounded measurable control $v$ is denominated ordinary. The proposed notion of solution is derived from a topological (non-metric) characterization of a former concept of solution which was given in the case when the drift is $v$-independent. Existence, uniqueness and representation of the solu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7726","kind":"arxiv","version":3},"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"}