A Turnpike Property for Optimal Control Problems with Dynamic Probabilistic Constraints
Gugat M, Henrion R, Heitsch H (2023)
Publication Type: Journal article, Original article
Publication year: 2023
Journal
Book Volume: 30
Pages Range: 1025--1052
Journal Issue: 3
URI: https://www.heldermann.de/JCA/JCA30/JCA303/jca30047.htm
Abstract
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 sufficient 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. In this way we contribute to the study of the turnpike phenomenon that is well-known in mathematical economics and make a step towards the extension of the turnpike theory to problems with probabilistic constraints.
Authors with CRIS profile
Martin Gugat
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
Germany (DE)How to cite
APA:
Gugat, M., Henrion, R., & Heitsch, H. (2023). A Turnpike Property for Optimal Control Problems with Dynamic Probabilistic Constraints. Journal of Convex Analysis, 30(3), 1025--1052.
MLA:
Gugat, Martin, René Henrion, and Holger Heitsch. "A Turnpike Property for Optimal Control Problems with Dynamic Probabilistic Constraints." Journal of Convex Analysis 30.3 (2023): 1025--1052.
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