{
  "id": "2209.08995",
  "version": "v1",
  "published": "2022-09-19T13:17:23.000Z",
  "updated": "2022-09-19T13:17:23.000Z",
  "title": "Data-Driven Control of Stochastic Systems: An Innovation Estimation Approach",
  "authors": [
    "Yibo Wang",
    "Chao Shang",
    "Dexian Huang"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "Recent years have witnessed a booming interest in the data-driven paradigm for predictive control. However, under noisy data ill-conditioned solutions could occur, causing inaccurate predictions and unexpected control behaviours. In this article, we explore a new route toward data-driven control of stochastic systems through active offline learning of innovation data, which gives an answer to the critical question of how to derive an optimal data-driven model from a noise-corrupted dataset. A generalization of the Willems' fundamental lemma is developed for non-parametric representation of input-output-innovation trajectories, provided realizations of innovation are precisely known. This yields a model-agnostic unbiased output predictor and paves the way for data-driven receding horizon control, whose behaviour is identical to the ``oracle\" solution of certainty-equivalent model-based control with measurable states. For efficient innovation estimation, a new low-rank subspace identification algorithm is developed. Numerical simulations show that by actively learning innovation from input-output data, remarkable improvement can be made over present formulations, thereby offering a promising framework for data-driven control of stochastic systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-19T13:17:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "data-driven control",
      "stochastic systems",
      "innovation estimation approach",
      "low-rank subspace identification algorithm",
      "noisy data ill-conditioned solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}