{
  "id": "1709.06487",
  "version": "v1",
  "published": "2017-09-19T15:27:00.000Z",
  "updated": "2017-09-19T15:27:00.000Z",
  "title": "A Simple and Efficient Algorithm for Nonlinear Model Predictive Control",
  "authors": [
    "Lorenzo Stella",
    "Andreas Themelis",
    "Pantelis Sopasakis",
    "Panagiotis Patrinos"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We present PANOC, a new algorithm for solving optimal control problems arising in nonlinear model predictive control (NMPC). A usual approach to this type of problems is sequential quadratic programming (SQP), which requires the solution of a quadratic program at every iteration and, consequently, inner iterative procedures. As a result, when the problem is ill-conditioned or the prediction horizon is large, each outer iteration becomes computationally very expensive. We propose a line-search algorithm that combines forward-backward iterations (FB) and Newton-type steps over the recently introduced forward-backward envelope (FBE), a continuous, real-valued, exact merit function for the original problem. The curvature information of Newton-type methods enables asymptotic superlinear rates under mild assumptions at the limit point, and the proposed algorithm is based on very simple operations: access to first-order information of the cost and dynamics and low-cost direct linear algebra. No inner iterative procedure nor Hessian evaluation is required, making our approach computationally simpler than SQP methods. The low-memory requirements and simple implementation make our method particularly suited for embedded NMPC applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-19T15:27:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear model predictive control",
      "efficient algorithm",
      "optimal control problems arising",
      "methods enables asymptotic superlinear rates",
      "inner iterative procedure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}