{
  "id": "2308.14265",
  "version": "v1",
  "published": "2023-08-28T02:46:15.000Z",
  "updated": "2023-08-28T02:46:15.000Z",
  "title": "A Risk-Aware Control: Integrating Worst-Case CVaR with Control Barrier Function",
  "authors": [
    "Masako Kishida"
  ],
  "comment": "under review",
  "categories": [
    "math.OC",
    "cs.SY",
    "eess.SY"
  ],
  "abstract": "This paper proposes a risk-aware control approach to enforce safety for discrete-time nonlinear systems subject to stochastic uncertainties. We derive some useful results on the worst-case Conditional Value-at-Risk (CVaR) and define a discrete-time risk-aware control barrier function using the worst-case CVaR. On this basis, we present optimization-based control approaches that integrate the worst-case CVaR into the control barrier function, taking into account both safe set and tail risk considerations. In particular, three types of safe sets are discussed in detail: half-space, polytope, and ellipsoid. It is shown that control inputs for the half-space and polytopic safe sets can be obtained via quadratic programs, while control inputs for the ellipsoidal safe set can be computed via a semidefinite program. Through numerical examples of an inverted pendulum, we compare its performance with existing methods and demonstrate the effectiveness of our proposed controller.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-28T02:46:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrating worst-case cvar",
      "safe set",
      "discrete-time risk-aware control barrier function",
      "control inputs",
      "discrete-time nonlinear systems subject"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}