{
  "abstract": "Layered control architectures provide a powerful paradigm for synthesizing controllers for complex systems. Yet, translating guarantees at each layer to system-level guarantees is challenging due to the interactions between layers. To address this problem, this paper presents a categorical perspective on layered control architectures. Individual systems are represented as control coalgebras, their interactions are specified as morphisms to mediators, and system-level behaviors are obtained via composition defined categorically as a pullback. To analyze the safety of these systems, we formulate control barrier morphisms (CBMs), the categorical generalization of control barrier functions. We prove that feedback controllers satisfying a CBM condition render the associated safe subobject forward invariant. It is through CBMs that we can establish the safety of layered systems: given a CBM at each layer subject to compatibility conditions, the universal property of the pullback implies the existence of a CBM for the composed system. Safety of a full-order model being safety filtered by a reduced-order model is recovered as a specialization of the categorical framework.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.38108",
  "author_total": 4,
  "authors": [
    {
      "name": "Aaron D. Ames"
    },
    {
      "name": "Joe Moeller"
    },
    {
      "name": "Massimiliano de Sa"
    },
    {
      "name": "Paulo Tabuada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7y4f7g9enw8q5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.38108",
  "fulltext_url": null,
  "id": "7y4f7g9enw8q5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.38108",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.38108",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7y4f7g9enw8q5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.38108",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.38108"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Safety of layered control systems via control barrier morphisms",
  "title_text": "Safety of layered control systems via control barrier morphisms",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/7y4f7g9enw8q5",
  "venue": "arXiv",
  "versions": []
}