{
  "id": "2108.03600",
  "version": "v1",
  "published": "2021-08-08T10:24:13.000Z",
  "updated": "2021-08-08T10:24:13.000Z",
  "title": "Pontryagin Maximum Principle for Distributed-Order Fractional Systems",
  "authors": [
    "Faical Ndairou",
    "Delfim F. M. Torres"
  ],
  "comment": "This is a preprint of a paper whose final and definite form is published Open Access in 'Mathematics', available in [https://doi.org/10.3390/math9161883]. Please cite this article as: F. Nda\\\"irou and D. F. M. Torres, Pontryagin Maximum Principle for Distributed-Order Fractional Systems, Mathematics 9 (2021), no. 16, Art. 1883, 12 pp",
  "journal": "Mathematics 9 (2021), no. 16, Art. 1883, 12 pp",
  "doi": "10.3390/math9161883",
  "categories": [
    "math.OC"
  ],
  "abstract": "We consider distributed-order non-local fractional optimal control problems with controls taking values on a closed set and prove a strong necessary optimality condition of Pontryagin type. The possibility that admissible controls are subject to pointwise constraints is new and requires more sophisticated techniques to include a maximality condition. We start by proving results on continuity of solutions due to needle-like control perturbations. Then, we derive a differentiability result on the state solutions with respect to the perturbed trajectories. We end by stating and proving the Pontryagin maximum principle for distributed-order fractional optimal control problems, illustrating its applicability with an example.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-08T10:24:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "49K15"
    ],
    "keywords": [
      "pontryagin maximum principle",
      "distributed-order fractional systems",
      "distributed-order non-local fractional optimal control",
      "non-local fractional optimal control problems",
      "distributed-order fractional optimal control problems"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}