{
  "id": "2303.17674",
  "version": "v1",
  "published": "2023-03-30T19:31:41.000Z",
  "updated": "2023-03-30T19:31:41.000Z",
  "title": "Exact Characterization of the Convex Hulls of Reachable Sets",
  "authors": [
    "Thomas Lew",
    "Riccardo Bonalli",
    "Marco Pavone"
  ],
  "categories": [
    "math.OC",
    "cs.LG",
    "cs.RO",
    "cs.SY",
    "eess.SY"
  ],
  "abstract": "We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing over-approximation tools tend to be conservative or computationally expensive. In this work, we exactly characterize the convex hulls of reachable sets as the convex hulls of solutions of an ordinary differential equation from all possible initial values of the disturbances. This finite-dimensional characterization unlocks a tight estimation algorithm to over-approximate reachable sets that is significantly faster and more accurate than existing methods. We present applications to neural feedback loop analysis and robust model predictive control.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-30T19:31:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "reachable sets",
      "convex hulls",
      "exact characterization",
      "neural feedback loop analysis",
      "ordinary differential equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}