{
  "id": "2208.13998",
  "version": "v1",
  "published": "2022-08-30T05:46:56.000Z",
  "updated": "2022-08-30T05:46:56.000Z",
  "title": "Value functional and optimal feedback control in linear-quadratic optimal control problem for fractional-order system",
  "authors": [
    "Mikhail I. Gomoyunov"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, a finite-horizon optimal control problem involving a dynamical system described by a linear Caputo fractional differential equation and a quadratic cost functional is considered. An explicit formula for the value functional is given, which includes a solution of a certain Fredholm integral equation. A step-by-step feedback control procedure for constructing $\\varepsilon$-optimal controls with any accuracy $\\varepsilon > 0$ is proposed. The basis for obtaining these results is the study of a solution of the associated Hamilton-Jacobi-Bellman equation with so-called fractional coinvariant derivatives.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-30T05:46:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "49N10",
      "34A08",
      "49L12",
      "49N35"
    ],
    "keywords": [
      "linear-quadratic optimal control problem",
      "optimal feedback control",
      "value functional",
      "fractional-order system",
      "linear caputo fractional differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}