{
  "abstract": "This paper studies the problem of optimal control of Caputo linear fractional-order systems of order $α\\in (0, 1]$ with continuous-time state constraints and input constraints. The resulting problems are semi-infinite, since the state constraints are imposed over the sampling intervals and not merely at the sampling instants. To address this, we derive a sampled-data representation of the inter-sample trajectory and use Bernstein polynomials to construct polytopic approximations of the continuous-time state constraints. Explicit bounds are obtained for the conservatism introduced by this approximation. By subdividing each sampling interval and applying the Bernstein-based construction on every subinterval, the approximation is made arbitrarily tight. Numerical examples illustrate the tightness of the proposed enclosures, the computational tractability of the proposed method, and the trade-off between approximation accuracy and computational complexity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12961",
  "author_total": 1,
  "authors": [
    {
      "name": "Pantelis Sopasakis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9dk45761d72z8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12961",
  "fulltext_url": null,
  "id": "9dk45761d72z8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12961",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Advanced Control Systems Design"
    ]
  ],
  "openalex": "W7212722178",
  "pdf_url": "https://arxiv.org/pdf/2609.12961",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9dk45761d72z8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12961",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12961"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Sampled-data optimal control of linear fractional-order systems",
  "title_text": "Sampled-data optimal control of linear fractional-order systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/9dk45761d72z8",
  "venue": "arXiv",
  "versions": []
}