{
  "abstract": "Motivated by batch and semi-batch process operation, we study finite-horizon open-loop dynamic optimization problems with uncertain parameters. A common computational approach replaces the expected performance criterion by an average over finitely many sampled parameter realizations. We develop a statistical theory for the resulting sample-based optimal value as an estimator of the population optimal value. The analysis is based on a stability estimate showing that terminal losses depend Lipschitz continuously on the time-integrated control, which records the cumulative input delivered up to each time. This estimate yields a functional central limit theorem for the sample-based objective and a statistical limit theorem for the corresponding optimal value error. As a consequence, we obtain confidence intervals for the population optimal value. When the population optimizer is unique, the limit is Gaussian and leads to a plug-in confidence interval. When multiple optimal policies may exist, we use a subsampling confidence interval that does not require uniqueness. The methodology is illustrated on two fed-batch case studies in which feed-rate profiles are optimized under parametric uncertainty.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.14965",
  "author_total": 2,
  "authors": [
    {
      "name": "Aurya Javeed"
    },
    {
      "name": "Johannes Milz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9rt9kd50kx25f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.14965",
  "fulltext_url": null,
  "id": "9rt9kd50kx25f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.14965",
  "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"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2207|Advanced Control Systems Optimization"
    ]
  ],
  "openalex": "W7169501576",
  "pdf_url": "https://arxiv.org/pdf/2607.14965",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9rt9kd50kx25f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2607.14965",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.14965"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Statistical Inference for Scenario-Based Dynamic Optimization under Uncertainty",
  "title_text": "Statistical Inference for Scenario-Based Dynamic Optimization under Uncertainty",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:29Z",
  "url": "https://research.draconitic.com/paper/9rt9kd50kx25f",
  "venue": "arXiv",
  "versions": []
}