{
  "abstract": "This paper studies a continuous-time probabilistic control problem for stochastic systems in which the feedback law assigns a probability distribution over control inputs. The control is modelled as a law-dependent Poisson-refresh process: it is held constant between refresh times and resampled at Poisson times from a feedback rule depending on the current state and state law. The closed-loop system is therefore formulated as a jump--diffusion for the joint state--control process. The objective is to design the sampling rule by comparing the realised closed-loop system with a prescribed reference description. The cost separates two local terms: a relative-entropy penalty for the instantaneous refresh kernel and a state-side drift-mismatch cost. The state-side term is evaluated at the realised control value and is motivated by a frozen-control Girsanov identity. Under global Lipschitz, moment, and uniform ellipticity assumptions, we prove well-posedness of the closed loop and a dynamic programming principle on the joint state--control law space. For linear data and admissible mean-dependent affine-Gaussian refresh rules, the full joint law need not remain Gaussian, but the first and second moments of the joint state--control process close exactly. This yields a deterministic reduced control problem on moment space, with an explicit running cost, a reduced Hamiltonian, and a verification theorem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06252",
  "author_total": 1,
  "authors": [
    {
      "name": "Randa Herzallah"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e2fe90c3z68wq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06252",
  "fulltext_url": null,
  "id": "e2fe90c3z68wq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06252",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06252",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e2fe90c3z68wq.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06252",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06252"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Law-Dependent Poisson-Refresh Randomised Feedback Control for Stochastic Systems",
  "title_text": "Law-Dependent Poisson-Refresh Randomised Feedback Control for Stochastic Systems",
  "type": "preprint",
  "updated_at": "2026-11-07T18:20:08Z",
  "url": "https://research.draconitic.com/paper/e2fe90c3z68wq",
  "venue": "arXiv",
  "versions": []
}