{
  "abstract": "Koopman model predictive control (MPC) iterates a lifted linear predictor over a horizon of tens of samples. Extended dynamic mode decomposition with control (EDMDc), however, fits that predictor by minimising only the one-step residual in the lifted space. This paper bounds the h-step output error of any lifted linear predictor by its one-step residual times an amplification factor Γh=∑j<h∥CAj∥2 that is computable from the model alone. The bound is attained for single-output systems, takes a horizon-uniform form through a scaled Lyapunov certificate, and extends to the suboptimality of the input sequence that MPC selects. The proposed HC-EDMDc minimises the rolled-out output error under a spectral-radius constraint, starts from the closed-form EDMDc solution as a warm start, and is selected by a held-out rolled-out criterion. The evaluation uses four measured benchmarks: a six-axis KUKA KR300 industrial robot, an electro-mechanical positioning system, a cascaded-tank process and the Silverbox oscillator. The one-step estimator returns a non-Schur transition matrix on 8 of 20 fits across 3 records, and its free run leaves the data range; the constraint removes this failure for at most 8.4 % of twenty-step accuracy. HC-EDMDc improves long-horizon accuracy on 2 records, reducing the twenty-step NRMSE on the cascaded tanks from 0.3431 for EDMDc + SR to 0.2827, and returns its warm start on the other 2; the size of the one-step residual does not predict which case a record falls into. Minimising εΓH collapses the predictor towards a mean-reverting model on 3 of the 4 records, and the certified bound moves opposite to the realised error on 2 of them. A valid bound is therefore not a model-selection criterion.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Data and Systems Engineering, The University of Hong Kong, Pokfulam, Hong Kong SAR, China",
    "Mechanical Engineering College, Xi’an Shiyou University, Xi’an 710065, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jia’en Zhang"
    },
    {
      "affs": [
        1
      ],
      "name": "Di Tian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0v243rvewvt6s.bib",
  "cited_by": 0,
  "doi": "10.3390/math14214047",
  "fulltext_url": null,
  "id": "0v243rvewvt6s",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/4047",
  "language": null,
  "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": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/0v243rvewvt6s.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T00:20:49Z",
      "native_id": "10.3390/math14214047",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/4047"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Error Amplification in Koopman Predictive Control: Computable Bounds, a Conditional Lyapunov Certificate, and Horizon-Consistent Estimation",
  "title_text": "Error Amplification in Koopman Predictive Control: Computable Bounds, a Conditional Lyapunov Certificate, and Horizon-Consistent Estimation",
  "type": "peer-reviewed",
  "updated_at": "2026-11-06T00:21:06Z",
  "url": "https://research.draconitic.com/paper/0v243rvewvt6s",
  "venue": "Mathematics",
  "versions": []
}