{
  "id": "1909.08380",
  "version": "v1",
  "published": "2019-09-18T11:59:15.000Z",
  "updated": "2019-09-18T11:59:15.000Z",
  "title": "Hamilton-Jacobi-Bellman Equation for Control Systems with Friction",
  "authors": [
    "Fabio Tedone",
    "Michele Palladino"
  ],
  "categories": [
    "math.OC",
    "math.DS"
  ],
  "abstract": "This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists in a controlled differential inclusion with a discontinuous right hand side, which still preserves existence and uniqueness of the solution for each given input function $u(t)$. Under general hypotheses, we are able to derive the Hamilton-Jacobi-Bellman equation for the related free time optimal control problem and to characterise the value function as the unique, locally Lipschitz continuous viscosity solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-18T11:59:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamilton-jacobi-bellman equation",
      "control systems",
      "lipschitz continuous viscosity solution",
      "free time optimal control problem",
      "related free time optimal control"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}