{
  "abstract": "This paper shows how a Schrodinger bridge (SB) structure emerges from maximum-entropy (MaxEnt) distribution steering of discrete-time nonlinear systems. We also establish that the resulting bridge can be realized by an optimal control policy. We consider general state and input costs, non-Gaussian endpoint distributions, and input constraints. Assuming the existence of a feasible policy with finite objective value, we show that the state-path measure under a MaxEnt optimal control policy is the unique SB. The reference measure of this SB is induced by an optimal policy of the corresponding terminal-unconstrained problem. Moreover, we give an equivalent characterization of the optimal state-path measure using a killed reference and its normalized Feynman--Kac measure, thereby interpreting the state cost as killing. We then characterize the finite-cost feasibility by the existence of an endpoint coupling having finite Kullback--Leibler divergence from the reference endpoint distribution. For compactly supported marginals with bounded target density, we derive reachability-based sufficient conditions guaranteeing this feasibility. We further provide specializations to fully actuated control-affine and reachable linear systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17965",
  "author_total": 2,
  "authors": [
    {
      "name": "Kaito Ito"
    },
    {
      "name": "Kenji Kashima"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2fb458t36jmgx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17965",
  "fulltext_url": null,
  "id": "2fb458t36jmgx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17965",
  "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",
      "2003|Stochastic processes and financial applications"
    ]
  ],
  "openalex": "W7221836111",
  "pdf_url": "https://arxiv.org/pdf/2610.17965",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2fb458t36jmgx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17965",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17965"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Control Realization of Schrödinger Bridges over Discrete-Time Nonlinear Systems via Maximum-Entropy Distribution Steering",
  "title_text": "Control Realization of Schrödinger Bridges over Discrete-Time Nonlinear Systems via Maximum-Entropy Distribution Steering",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/2fb458t36jmgx",
  "venue": "arXiv",
  "versions": []
}