{
  "abstract": "Can learned latent dynamics models support the design of feedback controllers that provably stabilize the original system? For linear time-invariant systems, we show that learning linear autoencoders and latent dynamics with multi-step prediction-reconstruction losses $\\unicode{x2014}$ which we term \"backward losses\" as they encourage latent trajectories to reconstruct full state trajectories $\\unicode{x2014}$ provably recovers the structure needed for stabilization. Specifically, a sufficiently long reconstruction horizon ensures that a minimum ${H}_\\infty$-norm controller designed using the learned latent model stabilizes the original system through output-feedback via the corresponding encoder, provided the latent dimension is large enough to capture all non-stable modes of the underlying system. We also show why both reconstruction and a multi-step horizon are essential: forward prediction losses that require only low prediction error along latent trajectories admit global loss minimizers that discard unstable modes regardless of horizon length, while single-step reconstruction losses can yield latent models whose stabilizing controllers fail to stabilize the original system. Finally, experiments on a non-linear flexible-arm system illustrate the practical implications of our results for learning non-linear autoencoders and latent dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40931",
  "author_total": 3,
  "authors": [
    {
      "name": "Paul Lutkus"
    },
    {
      "name": "Lars Lindemann"
    },
    {
      "name": "Stephen Tu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3abht5c0sqk3q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40931",
  "fulltext_url": null,
  "id": "3abht5c0sqk3q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40931",
  "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.LG"
    ],
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40931",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3abht5c0sqk3q.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.40931",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40931"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Learning Stabilizing Latent Feedback Controllers via Multi-Step Backward Losses",
  "title_text": "Learning Stabilizing Latent Feedback Controllers via Multi-Step Backward Losses",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/3abht5c0sqk3q",
  "venue": "arXiv",
  "versions": []
}