An aspect of the turnpike property. Long time horizon behavior
Gugat M, Sokolowski J (2023)
Publication Type: Journal article, Original article
Publication year: 2023
Journal
Serdica Mathematical Journal
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
Book Volume: 49
Pages Range: 127-154
Journal Issue: 1-3
URI: https://serdica.math.bas.bg/index.php/serdica/article/view/39
DOI: 10.55630/serdica.2023.49.127-154
Open Access Link: https://serdica.math.bas.bg/index.php/serdica/article/view/39/48
Abstract
The turnpike phenomenon concerns the structure of the optimal control and the optimal state of dynamic optimal control problems for long time horizons. The focus is regularly placed on the study of the interior of the time interval. Classical turnpike results state how the solution of the dynamic optimal control problems approaches the solution of the corresponding static optimal control problem in the interior of the time interval.
In this paper we look at a new aspect of the turnpike phenomenon. We show that for problems without explicit terminal condition, for large time horizons in the last part of the time interval the optimal state approaches a certain limit trajectory that is independent of the terminal time exponentially fast. For large time horizons also the optimal state in the initial part of the time interval approaches exponentially fast a limit state.
Authors with CRIS profile
Martin Gugat
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
Poland (PL)How to cite
APA:
Gugat, M., & Sokolowski, J. (2023). An aspect of the turnpike property. Long time horizon behavior. Serdica Mathematical Journal, 49(1-3), 127-154. https://dx.doi.org/10.55630/serdica.2023.49.127-154
MLA:
Gugat, Martin, and Jan Sokolowski. "An aspect of the turnpike property. Long time horizon behavior." Serdica Mathematical Journal 49.1-3 (2023): 127-154.
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