{
  "abstract": "We formulate and analyze the linear exponential quadratic Gaussian (LEQG) covariance steering problem in continuous time over a given deadline (finite time horizon). The solution for this problem can be seen as a risk-sensitive Schrödinger bridge between Gaussian endpoints in the linear quadratic setting. Unlike the risk-neutral case, the LEQG covariance steering controller--still a linear state feedback--can no longer be written in closed form. We show that the optimal controller is parameterized by a symmetric matrix solving an algebraic equation that encodes the implicit dependence on the risk-sensitivity parameter. We explain how the structure of this optimal controller significantly generalizes the existing results for the risk-neutral case. Building on these results, for the matched noise and input channel case, we prove the existence-uniqueness of solution for the LEQG covariance steering problem in the neighborhood of the known risk-neutral optimal solution. We give an illustrative numerical example.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12463",
  "author_total": 3,
  "authors": [
    {
      "name": "Chiran B. Cherian"
    },
    {
      "name": "Yasemin Isik"
    },
    {
      "name": "Abhishek Halder"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9e46j6m557rtb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12463",
  "fulltext_url": null,
  "id": "9e46j6m557rtb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12463",
  "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",
      "cs.AI"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2207|Advanced Control Systems Optimization"
    ]
  ],
  "openalex": "W7212875770",
  "pdf_url": "https://arxiv.org/pdf/2609.12463",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9e46j6m557rtb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12463",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12463"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Linear Exponential Quadratic Gaussian Covariance Steering",
  "title_text": "Linear Exponential Quadratic Gaussian Covariance Steering",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:17Z",
  "url": "https://research.draconitic.com/paper/9e46j6m557rtb",
  "venue": "arXiv",
  "versions": []
}