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

arXiv: https://arxiv.org/abs/2110.11021 · HTML: https://mlsanity.com/paper/2110.11021/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2021.

## Built on by (most cited first, 1 of 1)

- [Suboptimality analysis of receding horizon quadratic control with unknown linear systems and its applications in learning-based control](https://mlsanity.com/paper/2301.07876/) (2023)

## Abstract (arXiv)

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.