{
  "abstract": "We study constrained bilinear optimal control for nonlocal age--space structured population equations with renewal boundary conditions and endogenous surveillance feedback. The control acts as a coefficient in a mixed transport--diffusion equation, while a scalar observable generated by the state enters both the interior dynamics and the renewal law. This produces a nonlinear closed-loop control-to-state map and a feedback-dependent adjoint system. Using a characteristic mild formulation rather than a standard Lions--Magenes argument, we establish closed-loop well-posedness and Fréchet differentiability. We then derive the reduced and feedback-corrected adjoint equations. The feedback derivative is identified as a low-rank perturbation \\(\\ell_{\\bar y,\\bar u}(p)(t)χ(a,x)\\); in the Volterra-kernel regime, the associated transfer operator is quasinilpotent, yielding an explicit resolvent representation of the adjoint. Finally, we prove first-order optimality conditions and decompose the switching function into reduced and feedback-induced components.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.01347",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiguang Yu"
    },
    {
      "name": "Louis Shuo Wang"
    },
    {
      "name": "Ye Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/debsh7jvtaf4t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.01347",
  "fulltext_url": null,
  "id": "debsh7jvtaf4t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.01347",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7167274733",
  "pdf_url": "https://arxiv.org/pdf/2607.01347",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/debsh7jvtaf4t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2607.01347",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.01347"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Bilinear control of age--space structured populations",
  "title_text": "Bilinear control of age--space structured populations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/debsh7jvtaf4t",
  "venue": "arXiv",
  "versions": []
}