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arXiv · 2110.11021

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

Johannes Köhler·Melanie N. Zeilinger·Lars Grüne
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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.

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Johannes Köhler, Melanie N. Zeilinger, Lars Grüne. 2023-01-05. Stability and performance analysis of NMPC: Detectable stage costs and general terminal costs. https://doi.org/10.1109/tac.2023.3235244

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