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A turnpike property for optimal control problems with dynamic probabilistic constraints

  • In this paper we consider systems that are governed by linear time-discrete dynamics with an initial condition and a terminal condition for the expected values. We study optimal control problems where in the objective function a term of tracking type for the expected values and a control cost appear. In addition, the feasible states have to satisfy a conservative probabilistic constraint that requires that the probability that the trajectories remain in a given set F is greater than or equal to a given lower bound. An application are optimal control problems related to storage management systems with uncertain in- and output. We give suffcient conditions that imply that the optimal expected trajectories remain close to a certain state that can be characterized as the solution of an optimal control problem without prescribed initial- and terminal condition. Hence we contribute to the study of the turnpike phenomenon that is well-known in mathematical economics.

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Metadaten
Author:Martin Gugat, René Henrion, Holger Heitsch
Parent Title (German):Journal of Convex Analysis
Publisher:Heldermann Verlag 2023
Document Type:Article
Language:English
Date of Publication (online):2021/10/18
Date of first Publication:2021/10/18
Release Date:2021/10/18
Tag:Measure turnpike; Probabilistic Constraints; Probabilistic Robustness; Turnpike phenomenon; here-and-now decision
Volume:30
Issue:3
Page Number:27
First Page:1025
Last Page:1052
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B04
C03
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International