First results on turnpike bounds for stabilizing horizons in NMPC

Publikationstyp
Conference Paper
Publikationsdatum
2021-07-01
Sprache
English
Author
Pan, Guanru
Stomberg, Gösta
Engelmann, Alexander
Faulwasser, Timm 
TORE-URI
https://hdl.handle.net/11420/46160
Enthalten in
IFAC-PapersOnLine 
Volume
54
Issue
6
Start Page
153
End Page
158
Citation
IFAC-PapersOnLine 54 (6): 153-158 (2021)
Contribution to Conference
7th IFAC Conference on Nonlinear Model Predictive Control, NMPC 2021 
Publisher DOI
10.1016/j.ifacol.2021.08.538
Scopus ID
2-s2.0-85117950186
Publisher
IFAC
The stability analysis of NMPC schemes has seen significant progress in recent years, which includes schemes with and without terminal ingredients such as penalties and constraints. In the context of economic MPC, turnpike properties, which are closely related to dissipativity properties of the underlying optimal control problem, have enabled novel insights on stability conditions. In the present note, we show that turnpike properties naturally enable to bound the required stabilizing horizon length in MPC. The main idea is to define the turnpike with respect to a level-set of the terminal penalty. This way we derive a bound on the stabilizing horizon which guarantees that a terminal constraint is satisfied without being explicitly stated in the underlying optimal control problem. A numerical example indicates that if the terminal set is not too small, the horizon bound is not overly conservative.
Schlagworte
Model predictive control
Optimal control
Stability
Turnpike property
DDC Class
510: Mathematics
004: Computer Sciences