Stability and performance analysis of NMPC: Detectable stage costs and general terminal costs
arXiv:2110.11021 · doi:10.1109/TAC.2023.3235244
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.
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