Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 111393 |
| Seitenumfang | 14 |
| Fachzeitschrift | AUTOMATICA |
| Jahrgang | 159 |
| Frühes Online-Datum | 9 Nov. 2023 |
| Publikationsstatus | Veröffentlicht - Jan. 2024 |
Abstract
In this work, we study economic model predictive control (MPC) in situations where the optimal operating behavior is periodic. In such a setting, the performance of a standard economic MPC scheme without terminal conditions can generally be far from optimal even with arbitrarily long prediction horizons. Whereas there are modified economic MPC schemes that guarantee optimal performance, all of them are based on prior knowledge of the optimal period length or of the optimal periodic orbit itself. In contrast to these approaches, we propose to achieve optimality by multiplying the stage cost by a linear discount factor. This modification is not only easy to implement but also independent of any system- or cost-specific properties, making the scheme robust against online changes therein. Under standard dissipativity and controllability assumptions, we can prove that the resulting linearly discounted economic MPC without terminal conditions achieves optimal asymptotic average performance up to an error that vanishes with growing prediction horizons. Moreover, we can guarantee practical asymptotic stability of the optimal periodic orbit under the additional technical assumption that dissipativity holds with a continuous storage function. We complement these qualitative guarantees with a quantitative analysis of the transient and asymptotic average performance of the linearly discounted MPC scheme in a numerical simulation study.
ASJC Scopus Sachgebiete
- Ingenieurwesen (insg.)
- Steuerungs- und Systemtechnik
- Ingenieurwesen (insg.)
- Elektrotechnik und Elektronik
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in: AUTOMATICA, Jahrgang 159, 111393, 01.2024.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Linearly discounted economic MPC without terminal conditions for periodic optimal operation
AU - Schwenkel, Lukas
AU - Hadorn, Alexander
AU - Müller, Matthias A.
AU - Allgöwer, Frank
N1 - Funding Information: F. Allgöwer and M. A. Müller are thankful that this work was funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – AL 316/12-2 and MU 3929/1-2 – 279734922 . L. Schwenkel thanks the International Max Planck Research School for Intelligent Systems (IMPRS-IS) for supporting him. The material in this paper was partially presented at the 25th International Symposium on Mathematical Theory of Networks and Systems (MTNS), September 12–16, 2022, Bayreuth, Germany. This paper was recommended for publication in revised form by Associate Editor Marcello Farina under the direction of Editor Ian R. Petersen.
PY - 2024/1
Y1 - 2024/1
N2 - In this work, we study economic model predictive control (MPC) in situations where the optimal operating behavior is periodic. In such a setting, the performance of a standard economic MPC scheme without terminal conditions can generally be far from optimal even with arbitrarily long prediction horizons. Whereas there are modified economic MPC schemes that guarantee optimal performance, all of them are based on prior knowledge of the optimal period length or of the optimal periodic orbit itself. In contrast to these approaches, we propose to achieve optimality by multiplying the stage cost by a linear discount factor. This modification is not only easy to implement but also independent of any system- or cost-specific properties, making the scheme robust against online changes therein. Under standard dissipativity and controllability assumptions, we can prove that the resulting linearly discounted economic MPC without terminal conditions achieves optimal asymptotic average performance up to an error that vanishes with growing prediction horizons. Moreover, we can guarantee practical asymptotic stability of the optimal periodic orbit under the additional technical assumption that dissipativity holds with a continuous storage function. We complement these qualitative guarantees with a quantitative analysis of the transient and asymptotic average performance of the linearly discounted MPC scheme in a numerical simulation study.
AB - In this work, we study economic model predictive control (MPC) in situations where the optimal operating behavior is periodic. In such a setting, the performance of a standard economic MPC scheme without terminal conditions can generally be far from optimal even with arbitrarily long prediction horizons. Whereas there are modified economic MPC schemes that guarantee optimal performance, all of them are based on prior knowledge of the optimal period length or of the optimal periodic orbit itself. In contrast to these approaches, we propose to achieve optimality by multiplying the stage cost by a linear discount factor. This modification is not only easy to implement but also independent of any system- or cost-specific properties, making the scheme robust against online changes therein. Under standard dissipativity and controllability assumptions, we can prove that the resulting linearly discounted economic MPC without terminal conditions achieves optimal asymptotic average performance up to an error that vanishes with growing prediction horizons. Moreover, we can guarantee practical asymptotic stability of the optimal periodic orbit under the additional technical assumption that dissipativity holds with a continuous storage function. We complement these qualitative guarantees with a quantitative analysis of the transient and asymptotic average performance of the linearly discounted MPC scheme in a numerical simulation study.
KW - Economic model predictive control
KW - Optimal periodic operation
KW - Turnpike property
UR - http://www.scopus.com/inward/record.url?scp=85176270251&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2205.03118
DO - 10.48550/arXiv.2205.03118
M3 - Article
AN - SCOPUS:85176270251
VL - 159
JO - AUTOMATICA
JF - AUTOMATICA
SN - 0005-1098
M1 - 111393
ER -