{
  "id": "2305.03608",
  "version": "v1",
  "published": "2023-05-05T15:11:28.000Z",
  "updated": "2023-05-05T15:11:28.000Z",
  "title": "On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach",
  "authors": [
    "Alaa Eddine Chriat",
    "Chuangchuang Sun"
  ],
  "categories": [
    "cs.LG",
    "cs.RO",
    "cs.SY",
    "eess.SY",
    "math.OC"
  ],
  "abstract": "Safety has been a critical issue for the deployment of learning-based approaches in real-world applications. To address this issue, control barrier function (CBF) and its variants have attracted extensive attention for safety-critical control. However, due to the myopic one-step nature of CBF and the lack of principled methods to design the class-$\\mathcal{K}$ functions, there are still fundamental limitations of current CBFs: optimality, stability, and feasibility. In this paper, we proposed a novel and unified approach to address these limitations with Adaptive Multi-step Control Barrier Function (AM-CBF), where we parameterize the class-$\\mathcal{K}$ function by a neural network and train it together with the reinforcement learning policy. Moreover, to mitigate the myopic nature, we propose a novel \\textit{multi-step training and single-step execution} paradigm to make CBF farsighted while the execution remains solving a single-step convex quadratic program. Our method is evaluated on the first and second-order systems in various scenarios, where our approach outperforms the conventional CBF both qualitatively and quantitatively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-05T15:11:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "adaptive learning-based approach",
      "feasibility",
      "optimality",
      "single-step convex quadratic program",
      "adaptive multi-step control barrier function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}