{
  "id": "2109.13359",
  "version": "v2",
  "published": "2021-09-27T21:42:19.000Z",
  "updated": "2022-08-17T20:51:47.000Z",
  "title": "Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximation",
  "authors": [
    "Nathan Gaby",
    "Fumin Zhang",
    "Xiaojing Ye"
  ],
  "comment": "Accepted to 61st IEEE Conference on Decision and Control",
  "categories": [
    "cs.LG",
    "math.OC"
  ],
  "abstract": "We develop a versatile deep neural network architecture, called Lyapunov-Net, to approximate Lyapunov functions of dynamical systems in high dimensions. Lyapunov-Net guarantees positive definiteness, and thus it can be easily trained to satisfy the negative orbital derivative condition, which only renders a single term in the empirical risk function in practice. This significantly reduces the number of hyper-parameters compared to existing methods. We also provide theoretical justifications on the approximation power of Lyapunov-Net and its complexity bounds. We demonstrate the efficiency of the proposed method on nonlinear dynamical systems involving up to 30-dimensional state spaces, and show that the proposed approach significantly outperforms the state-of-the-art methods.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-08-17T20:51:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lyapunov function approximation",
      "versatile deep neural network architecture",
      "approximate lyapunov functions",
      "dynamical systems",
      "lyapunov-net guarantees positive definiteness"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}