{
  "id": "2101.06350",
  "version": "v1",
  "published": "2021-01-16T02:23:37.000Z",
  "updated": "2021-01-16T02:23:37.000Z",
  "title": "Exponential Decay of Sensitivity in Nonlinear Model Predictive Control: A Graph-Theoretic Approach",
  "authors": [
    "Sungho Shin",
    "Victor M. Zavala"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "Exponential decay of sensitivity (EDS) is a property of nonlinear model predictive control (NMPC) problems; the property indicates that the sensitivity of the solution at time $i$ against a data perturbation at time $j$ decays exponentially with $|i-j|$. We use a graph-theoretic analysis of the optimality conditions of NMPC problems to prove that EDS holds under uniform boundedness of the Lagrangian Hessian, a uniform second order sufficiency condition (uSOSC), and a uniform linear independence constraint qualification (uLICQ). Furthermore, we prove that uSOSC and uLICQ can be obtained from uniform controllability and observability (well-known system-theoretic properties). These results provide insights into how perturbations propagate along the horizon and enable the development of approximation and solution schemes. We illustrate the developments with numerical examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-16T02:23:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear model predictive control",
      "exponential decay",
      "graph-theoretic approach",
      "sensitivity",
      "uniform linear independence constraint qualification"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}