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Faulwasser, Timm ; Grüne, Lars ; Humaloja, Jukka-Pekka ; Schaller, Manuel:
The interval turnpike property for adjoints.
In: Pure and Applied Functional Analysis.
Bd. 7
(2022)
Heft 4
.
- S. 1187-1207.
ISSN 2189-3756
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| Projekttitel: |
Offizieller Projekttitel Projekt-ID Specialized Adaptive Algorithms for Model Predictive Control of PDEs GR 1569/17-1 Specialized Adaptive Algorithms for Model Predictive Control of PDEs SCHI 1379/5-1 The research was conducted while the third author was visiting University of Bayreuth under Academy of Finland Grant number 310489 held by Lassi Paunonen and supported by a travel grantfrom the Magnus Ehrnrooth Foundation Ohne Angabe |
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Deutsche Forschungsgemeinschaft |
Abstract
In this work we derive an interval turnpike result for adjoints of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further give stronger estimates for analytic semigroups and provide a numerical example with a boundary controlled semilinear heat equation to illustrate the results.
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The interval turnpike property for adjoints. (deposited 27 Mai 2020 07:42)
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