{
  "id": "2310.10619",
  "version": "v1",
  "published": "2023-10-16T17:42:25.000Z",
  "updated": "2023-10-16T17:42:25.000Z",
  "title": "Shortest-path recovery from signature with an optimal control approach",
  "authors": [
    "Marco Rauscher",
    "Alessandro Scagliotti",
    "Felipe Pagginelli"
  ],
  "comment": "25 pages, 5 figures",
  "categories": [
    "math.OC",
    "cs.NA",
    "cs.SY",
    "eess.SY",
    "math.NA"
  ],
  "abstract": "In this paper, we consider the signature-to-path reconstruction problem from the control theoretic perspective. Namely, we design an optimal control problem whose solution leads to the minimal-length path that generates a given signature. In order to do that, we minimize a cost functional consisting of two competing terms, i.e., a weighted final-time cost combined with the $L^2$-norm squared of the controls. Moreover, we can show that, by taking the limit to infinity of the parameter that tunes the final-time cost, the problem $\\Gamma$-converges to the problem of finding a sub-Riemannian geodesic connecting two signatures. Finally, we provide an alternative reformulation of the latter problem, which is particularly suitable for the numerical implementation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-16T17:42:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimal control approach",
      "shortest-path recovery",
      "optimal control problem",
      "signature-to-path reconstruction problem",
      "minimal-length path"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}