{
  "abstract": "We study an optimal actuator design problem for infinite-horizon LQ control problems governed by parabolic equations. The control acts only on a small measurable subregion of the spatial domain, and the objective combines the infinite-horizon control value with a cost for the actuator region. Using the Riccati representation of the value function, we derive a comparison identity for two actuator supports and obtain an exact expansion of the objective. This leads to a topological derivative with respect to local changes in the support. We prove a localized Riccati sensitivity estimate to control the remainder and show that the infinite-horizon term in the derivative can be computed by solving a Lyapunov equation. This yields a computable support-update algorithm with a measure-controlled Armijo search. Under explicit uniform remainder and admissibility assumptions, its first-order stationarity defect tends to zero. Numerical experiments illustrate these results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.12553",
  "author_total": 2,
  "authors": [
    {
      "name": "Behzad Azmi"
    },
    {
      "name": "Daniel Wachsmuth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d6k6rbqz6byna.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.12553",
  "fulltext_url": null,
  "id": "d6k6rbqz6byna",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.12553",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.12553",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d6k6rbqz6byna.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:37Z",
      "native_id": "2611.12553",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.12553"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Optimal Actuator Support Design for Infinite-Horizon Linear-Quadratic Parabolic Control Problems",
  "title_text": "Optimal Actuator Support Design for Infinite-Horizon Linear-Quadratic Parabolic Control Problems",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:37Z",
  "url": "https://research.draconitic.com/paper/d6k6rbqz6byna",
  "venue": "arXiv",
  "versions": []
}