{"paper":{"title":"Mean-Field Sparse Jurdjevic--Quinn Control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Benedetto Piccoli, Emmanuel Tr\\'elat (UPMC, Francesco Rossi (LSIS), LJLL), Marco Caponigro (M2N)","submitted_at":"2017-01-05T13:57:46Z","abstract_excerpt":"We consider nonlinear transport equations with non-local velocity, describing the time-evolution of a measure, which in practice may represent the density of a crowd. Such equations often appear by taking the mean-field limit of finite-dimensional systems modelling collective dynamics. We first give a sense to dissipativity of these mean-field equations in terms of Lie derivatives of a Lyapunov function depending on the measure. Then, we address the problem of controlling such equations by means of a time-varying bounded control action localized on a time-varying control subset with bounded Le"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.01316","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"}