English

Stability and performance analysis of NMPC: Detectable stage costs and general terminal costs

Optimization and Control 2023-01-09 v3 Systems and Control Systems and Control

Abstract

We provide a stability and performance analysis for nonlinear model predictive control (NMPC) schemes subject to input constraints. Given an exponential stabilizability and detectability condition w.r.t. the employed state cost, we provide a sufficiently long prediction horizon to ensure asymptotic stability and a desired performance bound w.r.t. the infinite-horizon optimal controller. Compared to existing results, the provided analysis is applicable to positive semi-definite (detectable) cost functions, provides tight bounds using a linear programming analysis, and allows for a seamless integration of general positive-definite terminal cost functions in the analysis. The practical applicability of the derived theoretical results are demonstrated with numerical examples.

Keywords

Cite

@article{arxiv.2110.11021,
  title  = {Stability and performance analysis of NMPC: Detectable stage costs and general terminal costs},
  author = {Johannes Köhler and Melanie N. Zeilinger and Lars Grüne},
  journal= {arXiv preprint arXiv:2110.11021},
  year   = {2023}
}

Comments

This is the accepted version of the paper in IEEE Transaction on Automatic Control, 2023. This version contains additionally the proof of Theorem 7 in the appendix