{
  "abstract": "We study finite-horizon distributionally robust linear-quadratic control with disturbances that can be arbitrarily correlated in time. The ambiguity set is modeled as a single 2-Wasserstein ball centered at a nominal elliptically contoured distribution of the disturbances. Despite the infinite-dimensionality of both the policy space and ambiguity set, we prove that the optimal policy is affine and that the worst-case distribution is an affine push-forward of the nominal distribution. These affine maps can be computed efficiently via a best-response algorithm based on the Frank--Wolfe algorithm. Experiments demonstrate improved out-of-sample performance over LQG and its distributionally robust extensions when the true disturbances are correlated, incurring only a small loss of performance under uncorrelated disturbances.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27653",
  "author_total": 4,
  "authors": [
    {
      "name": "Jakob Nylöf"
    },
    {
      "name": "Daniel Kuhn"
    },
    {
      "name": "John Lygeros"
    },
    {
      "name": "Giancarlo Ferrari-Trecate"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2z4cdxs1fexgr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27653",
  "fulltext_url": null,
  "id": "2z4cdxs1fexgr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27653",
  "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",
      "1803|Risk and Portfolio Optimization"
    ]
  ],
  "openalex": "W7214147025",
  "pdf_url": "https://arxiv.org/pdf/2609.27653",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2z4cdxs1fexgr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27653",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27653"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Optimality of Affine Policies in Distributionally Robust Linear-Quadratic Control with Temporally Correlated Noise",
  "title_text": "Optimality of Affine Policies in Distributionally Robust Linear-Quadratic Control with Temporally Correlated Noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/2z4cdxs1fexgr",
  "venue": "arXiv",
  "versions": []
}