{
  "abstract": "We investigate the stability and near-optimality properties of deterministic discrete-time systems whose inputs are generated by policy iteration (PI) considering a discounted infinite-horizon cost function. We leverage the discounting of the cost to initialize PI with policies that may not be stabilizing. Novel bounds are first established on the difference between the cost induced by a policy generated by PI at each iteration and the optimal value function, which are typically tighter than those encountered in the dynamic programming literature for the considered set-up. Under general assumptions, we then prove that the systems whose inputs are given by a policy generated by PI satisfy a semiglobal practical stability for discount factors sufficiently close to 1 and after a finite number of iterations that we can estimate. Global exponential stability is also ensured under strengthened assumptions. The theoretical findings are illustrated via examples and two notable case studies: the discounted linear quadratic regulator and the discounted absolute value bound problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "name": "Jonathan de Brusse"
    },
    {
      "name": "Mathieu Granzotto"
    },
    {
      "name": "Romain Postoyan"
    },
    {
      "name": "Dragan Nešić"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2vddv87w42894.bib",
  "cited_by": 0,
  "doi": "10.1016/j.automatica.2026.113158",
  "fulltext_url": null,
  "id": "2vddv87w42894",
  "issns": [
    "0005-1098"
  ],
  "landing_url": "https://hal.science/hal-05731949v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
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      "hal",
      "0.spi"
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      "hal",
      "1.math.math-oc"
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      "1703|Adaptive Dynamic Programming Control"
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  "openalex": "W7167920322",
  "pdf_url": "https://hal.science/hal-05731949/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/2vddv87w42894.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:21Z",
      "native_id": "hal-05731949",
      "source": "hal",
      "url": "https://hal.science/hal-05731949v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Policy iteration with discounted cost: near-optimality bounds and stability guarantees ⋆",
  "title_text": "Policy iteration with discounted cost: near-optimality bounds and stability guarantees ⋆",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:21Z",
  "url": "https://research.draconitic.com/paper/2vddv87w42894",
  "venue": "Automatica",
  "versions": []
}