{"paper":{"title":"Optimal growth for linear processes with affine control","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.OC"],"primary_cat":"math.AP","authors_text":"Pierre Gabriel (LJLL), Vincent Calvez (UMPA-ENSL)","submitted_at":"2012-03-23T07:15:06Z","abstract_excerpt":"We analyse an optimal control with the following features: the dynamical system is linear, and the dependence upon the control parameter is affine. More precisely we consider $\\dot x_\\alpha(t) = (G + \\alpha(t) F)x_\\alpha(t)$, where $G$ and $F$ are $3\\times 3$ matrices with some prescribed structure. In the case of constant control $\\alpha(t)\\equiv \\alpha$, we show the existence of an optimal Perron eigenvalue with respect to varying $\\alpha$ under some assumptions. Next we investigate the Floquet eigenvalue problem associated to time-periodic controls $\\alpha(t)$. Finally we prove the existenc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5189","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"}