{
  "id": "2209.08728",
  "version": "v1",
  "published": "2022-09-19T02:54:29.000Z",
  "updated": "2022-09-19T02:54:29.000Z",
  "title": "Control Barrier Functions for Stochastic Systems With Quantitative Evaluation of Probability",
  "authors": [
    "Yuki Nishimura",
    "Kenta Hoshino"
  ],
  "comment": "22 pages, 10 figures",
  "categories": [
    "math.OC",
    "cs.SY",
    "eess.SY",
    "math.DS"
  ],
  "abstract": "In recent years, the analysis of a control barrier function has received considerable attention because it is helpful for the safety-critical control required in many control application problems. However, the extension of the analysis to a stochastic system remains a challenging issue. In this paper, we consider sufficient conditions for almost-sure-type reciprocal and zeroing control barrier functions and design a control law. Then, we propose another version of a stochastic zeroing control barrier function to evaluate a probability of a sample path staying in a safe set and confirm the convergence of a specific expectation related to the attractiveness of a safe set. We also discuss the robustness of safety against changing a diffusion coefficient. Finally, we confirm the validity of the proposed control design and the analysis using the control barrier functions via simple examples with their numerical simulation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-19T02:54:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantitative evaluation",
      "probability",
      "safe set",
      "stochastic zeroing control barrier function",
      "stochastic system remains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}