{
  "abstract": "In this paper, we tackle the problem of computing safe controllers for nonlinear dynamical systems, extending previous work on linear systems that relied on probabilistic abstraction. Building an exact probabilistic abstraction of a nonlinear system requires computing exact reachable sets, a task that is known to be infeasible for such systems. To overcome this limitation, we rely on over-approximations of reachable sets. The probabilistic approximation is formally a Markov Decision Process (MDP). To enhance scalability, the MDP is stored as a Dynamic Bayesian Network (DBN), this formulation allows for a compact representation of the probabilistic abstraction. Controllers can then be derived using reinforcement learning (RL) techniques such as policy iteration. Their safety is ensured by using reachability over-approximations to determine which control modes are admissible. The RL problem is then restricted to these safe modes. Finally, we illustrate our framework on a path planning problem in a maze environment.",
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  "article_type": null,
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  "author_total": 4,
  "authors": [
    {
      "name": "Yahia Bahloul"
    },
    {
      "name": "Adrien Le Coënt"
    },
    {
      "name": "Benoît Barbot"
    },
    {
      "name": "Nihal Pekergin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5b22pq25zj2t5.bib",
  "cited_by": 0,
  "doi": null,
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  "id": "5b22pq25zj2t5",
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  "landing_url": "https://hal.science/hal-05837173v1",
  "language": "en",
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": null,
  "native_subjects": [
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    ],
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      "hal",
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05837173/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5b22pq25zj2t5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05837173",
      "source": "hal",
      "url": "https://hal.science/hal-05837173v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ds",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Safe Controller Synthesis for Nonlinear Switched Systems via Probabilistic Abstractions",
  "title_text": "Safe Controller Synthesis for Nonlinear Switched Systems via Probabilistic Abstractions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/5b22pq25zj2t5",
  "venue": "HAL",
  "versions": []
}