{
  "id": "2210.12312",
  "version": "v1",
  "published": "2022-10-22T00:29:58.000Z",
  "updated": "2022-10-22T00:29:58.000Z",
  "title": "Bounded-Regret MPC via Perturbation Analysis: Prediction Error, Constraints, and Nonlinearity",
  "authors": [
    "Yiheng Lin",
    "Yang Hu",
    "Guannan Qu",
    "Tongxin Li",
    "Adam Wierman"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We study Model Predictive Control (MPC) and propose a general analysis pipeline to bound its dynamic regret. The pipeline first requires deriving a perturbation bound for a finite-time optimal control problem. Then, the perturbation bound is used to bound the per-step error of MPC, which leads to a bound on the dynamic regret. Thus, our pipeline reduces the study of MPC to the well-studied problem of perturbation analysis, enabling the derivation of regret bounds of MPC under a variety of settings. To demonstrate the power of our pipeline, we use it to generalize existing regret bounds on MPC in linear time-varying (LTV) systems to incorporate prediction errors on costs, dynamics, and disturbances. Further, our pipeline leads to regret bounds on MPC in systems with nonlinear dynamics and constraints.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-22T00:29:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "perturbation analysis",
      "bounded-regret mpc",
      "regret bounds",
      "constraints",
      "dynamic regret"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}