{"paper":{"title":"Fejer Polynomials and Control of Nonlinear Discrete Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Stokolos, Anatolii Korenovskyi, Anna Khamitova, Dmitriy Dmitrishin, Paul Hagelstein","submitted_at":"2018-04-12T14:37:39Z","abstract_excerpt":"We consider optimization problems associated to a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizing $T$-cycles of a differentiable function $f: \\mathbb{R}\\rightarrow\\mathbb{R}$ of the form $$x(k+1) = f(x(k)) + u(k)$$ where $$u(k) = (a_1 - 1)f(x(k)) + a_2 f(x(k-T)) + \\cdots + a_N f(x(k-(N-1)T))\\;,$$ with $a_1 + \\cdots + a_N = 1$. Following an approach of Morg\\\"ul, we associate to each periodic orbit of $f$, $N \\in \\mathbb{N}$, and $a_1,\\ldots,a_N$ an explicit polynomial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04537","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"}