{
  "abstract": "The open-loop minimum-energy control (MEC) problem asks for control inputs that minimize the control energy while ensuring the terminal state reaches a desired value. In this paper, we study the open-loop MEC problem for stochastic linear time-invariant systems. We consider a variety of stochastic constraints that enforce the terminal error to be small, and show that Stochastic MEC (SMEC) problem can be formulated as a QCQP. We obtain the optimal solution for SMEC and show that it generalizes the well-known Deterministic MEC problem by introducing novel stochastic variants of controllability and Gramian matrices. When the system dynamics is unknown, we obtain a direct data-driven solution to the SMEC problem using maximum-likelihood estimation and conformal calibration approaches. Finally, we quantify the sub-optimality and constraint violation of our data-driven solutions via finite-sample high-probability upper bounds, and highlight their dependence on the number of experiments, system dimension, and noise-to-signal ratio. We present numerical simulations to validate the theoretical results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27599",
  "author_total": 2,
  "authors": [
    {
      "name": "Vaishnavi Sharma"
    },
    {
      "name": "Vaibhav Katewa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pc9dbp50ff65.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27599",
  "fulltext_url": null,
  "id": "8pc9dbp50ff65",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27599",
  "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.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Advanced Control Systems Optimization"
    ]
  ],
  "openalex": "W7223119114",
  "pdf_url": "https://arxiv.org/pdf/2610.27599",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pc9dbp50ff65.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.27599",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27599"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Minimum-Energy Control for Stochastic Linear Systems: A Data-Driven Approach with Finite-Sample Guarantees",
  "title_text": "Minimum-Energy Control for Stochastic Linear Systems: A Data-Driven Approach with Finite-Sample Guarantees",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/8pc9dbp50ff65",
  "venue": "arXiv",
  "versions": []
}