Towards necessary and sufficient stability conditions for NMPC

Publikationstyp
Conference Paper
Date Issued
2021-07-01
Sprache
English
Author(s)
Faulwasser, Timm  
TORE-URI
https://hdl.handle.net/11420/46161
Journal
IFAC-PapersOnLine  
Volume
54
Issue
6
Start Page
139
End Page
146
Citation
IFAC-PapersOnLine 54 (6): 139-146 (2021)
Contribution to Conference
7th IFAC Conference on Nonlinear Model Predictive Control, NMPC 2021  
Publisher DOI
10.1016/j.ifacol.2021.08.536
Scopus ID
2-s2.0-85117932415
Publisher
IFAC
The analysis of convergence and stability conditions for Non-linear Model Predictive Control (NMPC) schemes has seen significant progress during the last decades. Numerous results in the literature state sufficient conditions for convergence and/or stability of NMPC. Yet, necessary and sufficient conditions are—to the best of the author's knowledge—not known and, given the variety of choices for MPC design, seemingly appear to be difficult. This paper analyzes the convergence of NMPC of continuous-time systems in time-invariant settings. We introduce the receding-horizon Hamiltonian—i.e., the value of the optimal control Hamiltonian along the sequence of OCPs—as a novel tool for stability/convergence analysis. Based on the assumption of strict dissipativity, we prove necessary and sufficient conditions for asymptotic convergence of the closed loop to the optimal steady state. Numerical results obtained for the Van de Vusse reactor illustrate the proposed conditions.
Subjects
Asymptotic convergence
Dissipativity
Model predictive control
Necessary conditions of optimality
Optimal control
Stability
DDC Class
510: Mathematics
004: Computer Sciences