{
  "id": "2203.11510",
  "version": "v1",
  "published": "2022-03-22T07:37:57.000Z",
  "updated": "2022-03-22T07:37:57.000Z",
  "title": "Continuous Optimization for Control of Hybrid Systems with Hysteresis via Time-Freezing",
  "authors": [
    "Armin Nurkanović",
    "Moritz Diehl"
  ],
  "comment": "Submitted to the The IEEE Control Systems Letters and the IEEE Conference on Decision and Control",
  "categories": [
    "math.OC",
    "cs.SY",
    "eess.SY"
  ],
  "abstract": "This article regards numerical optimal control of a class of hybrid systems with hysteresis using solely techniques from nonlinear optimization, without any integer variables. Hysteresis is a rate independent memory effect which often results in severe nonsmoothness in the dynamics. These systems are not simply Piecewise Smooth Systems (PSS); they are a more complicated form of hybrid systems. We introduce a time-freezing reformulation which transforms these systems into a PSS. From the theoretical side, this reformulation opens the door to study systems with hysteresis via the rich tools developed for Filippov systems. From the practical side, it enables the use of the recently developed Finite Elements with Switch Detection [Nurkanovic et al., 2022], which makes high accuracy numerical optimal control of hybrid systems with hysteresis possible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-22T07:37:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hybrid systems",
      "hysteresis",
      "continuous optimization",
      "article regards numerical optimal control",
      "rate independent memory effect"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}