{
  "abstract": "Optimal Control Problems (OCPs) have been applied to a variety of applications. Such problems are often transcribed into a Nonlinear Program (NLP) for which solution methods typically solve a Linear Quadratic (LQ) subproblem. To efficiently solve this LQ subproblem, the Riccati recursion exploits the block-diagonal structure that arises from discretizing an OCP using a Multiple Shooting method. However, reformulating general dynamics constraints to fit the required problem structure to use the Riccati recursion introduces additional micro-structure within these block matrices that remains unexploited. This work demonstrates how structure-exploiting solvers such as Fatrop can benefit from exploiting not only the block-diagonal structure but also the micro-structure within those blocks. We propose a structure-exploiting LU decomposition algorithm and integrate it within the Riccati recursion. Numerical results on randomized linear systems and two OCP examples demonstrate a reduction in computation time of the search direction of up to 20%, with the largest speedup observed for relative zero block sizes around 0.25 and large stage-wise equality constraint jacobians.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29238",
  "author_total": 2,
  "authors": [
    {
      "name": "Louis Callens"
    },
    {
      "name": "Wilm Decré"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3c0vdkx9kpdc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29238",
  "fulltext_url": null,
  "id": "b3c0vdkx9kpdc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29238",
  "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",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Advanced Control Systems Optimization"
    ]
  ],
  "openalex": "W7204966031",
  "pdf_url": "https://arxiv.org/pdf/2608.29238",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3c0vdkx9kpdc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29238",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29238"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Exploiting Micro-Structure in the Generalized Riccati Recursion for Optimal Control",
  "title_text": "Exploiting Micro-Structure in the Generalized Riccati Recursion for Optimal Control",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/b3c0vdkx9kpdc",
  "venue": "arXiv",
  "versions": []
}