{
  "id": "2204.05551",
  "version": "v1",
  "published": "2022-04-12T06:31:26.000Z",
  "updated": "2022-04-12T06:31:26.000Z",
  "title": "Near-Optimal Distributed Linear-Quadratic Regulator for Networked Systems",
  "authors": [
    "Sungho Shin",
    "Yiheng Lin",
    "Guannan Qu",
    "Adam Wierman",
    "Mihai Anitescu"
  ],
  "categories": [
    "math.OC",
    "cs.LG",
    "cs.SY",
    "eess.SY",
    "math.DS"
  ],
  "abstract": "This paper studies the trade-off between the degree of decentralization and the performance of a distributed controller in a linear-quadratic control setting. We study a system of interconnected agents over a graph and a distributed controller, called $\\kappa$-distributed control, which lets the agents make control decisions based on the state information within distance $\\kappa$ on the underlying graph. This controller can tune its degree of decentralization using the parameter $\\kappa$ and thus allows a characterization of the relationship between decentralization and performance. We show that under mild assumptions, including stabilizability, detectability, and a polynomially growing graph condition, the performance difference between $\\kappa$-distributed control and centralized optimal control becomes exponentially small in $\\kappa$. This result reveals that distributed control can achieve near-optimal performance with a moderate degree of decentralization, and thus it is an effective controller architecture for large-scale networked systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-12T06:31:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "near-optimal distributed linear-quadratic regulator",
      "networked systems",
      "decentralization",
      "distributed controller",
      "achieve near-optimal performance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}