{
  "id": "2210.06053",
  "version": "v1",
  "published": "2022-10-12T09:46:29.000Z",
  "updated": "2022-10-12T09:46:29.000Z",
  "title": "Sensitivity analysis of value functional of fractional optimal control problem with application to construction of optimal feedback control",
  "authors": [
    "Mikhail Gomoyunov"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We consider an optimal control problem for a dynamical system described by a Caputo fractional differential equation and a terminal cost functional. We prove that, under certain assumptions, the (non-smooth, in general) value functional of this problem has a property of directional differentiability of order $\\alpha$. As an application of this result, we propose a new method for constructing an optimal positional (feedback) control strategy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-12T09:46:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49N35",
      "34A08",
      "49L12",
      "49J52"
    ],
    "keywords": [
      "fractional optimal control problem",
      "optimal feedback control",
      "value functional",
      "sensitivity analysis",
      "application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}