{
  "abstract": "This paper develops a data-driven realization of the generalized Koopman operator (GeKo) [1], in which states and inputs are lifted independently and the dynamics are expressed as a tensor bilinear system. The first contribution is a time-sequenced multi-step Khatri-Rao kernel regression formulation that exposes the operator to evolved snapshots along trajectories rather than only single one-step pairs, which reduces compounded prediction error. Secondly, we develop a kernel- and input-agnostic structured SVD reduction that compresses the lifted state and input spaces while preserving the Khatri-Rao realization. We instantiate the framework with random Fourier features and describe a complete predictive-control pipeline, including a multi-step roll-out diagnostic that guides the choice of MPC horizon. The framework is validated on the chaotic Lorenz system, where the learned reduced-order GeKo model reduces the long-horizon prediction error by up to a factor of five relative to one-step and lifted linear baselines fitted on the same data, and stabilizes an unstable equilibrium.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.02938",
  "author_total": 1,
  "authors": [
    {
      "name": "Mircea Lazar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27g4gx7gt7y5j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.02938",
  "fulltext_url": null,
  "id": "27g4gx7gt7y5j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.02938",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7163353722",
  "pdf_url": "https://arxiv.org/pdf/2606.02938",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27g4gx7gt7y5j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2606.02938",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.02938"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Koopman operator learning for predictive control via Khatri-Rao kernel regression",
  "title_text": "Koopman operator learning for predictive control via Khatri-Rao kernel regression",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/27g4gx7gt7y5j",
  "venue": "arXiv",
  "versions": []
}