{
  "id": "2405.14461",
  "version": "v1",
  "published": "2024-05-23T11:49:59.000Z",
  "updated": "2024-05-23T11:49:59.000Z",
  "title": "A Power Tower Control: A New Sliding Mode Control",
  "authors": [
    "Malek Ghanes",
    "Jean-Pierre Barbot"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "A control based power tower function at order 2 is proposed in this paper. This leads to a new sliding mode control, which allows employing backstepping technique that combines both guaranteed and finite time convergence. The proposed control is applied to a double integrator subject to perturbation $d$. Both guaranteed and finite convergence are ensured by the controller when $d$ is considered constant and bounded, without knowing its upper bound. For the case, when $d$ is variable and bounded with its upper bound known, only a finite time convergence is obtained. Simulation results are given to show the well founded of the proposed novel control.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-23T11:49:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sliding mode control",
      "power tower control",
      "finite time convergence",
      "upper bound",
      "power tower function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}