{
  "id": "2309.08280",
  "version": "v1",
  "published": "2023-09-15T09:48:39.000Z",
  "updated": "2023-09-15T09:48:39.000Z",
  "title": "Relaxation and asymptotic expansion of controlled stiff differential equations",
  "authors": [
    "Michael Herty",
    "Hicham Kouhkouh"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. It is shown that their solution also allows for an asymptotic expansion in the relaxation parameter. For the first-order expansion, its solution converges toward the solution to a Hamilton-Jacobi-Bellman equation for a reduced control problem. The considered systems are motivated by semi-discretization of kinetic and hyperbolic partial differential equations and several examples are presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-15T09:48:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34H05",
      "35F21"
    ],
    "keywords": [
      "controlled stiff differential equations",
      "asymptotic expansion",
      "hamilton-jacobi-bellman equation",
      "hyperbolic partial differential equations",
      "ordinary differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}