| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 6 | |
| Number of page(s) | 38 | |
| DOI | https://doi.org/10.1051/cocv/2024080 | |
| Published online | 06 January 2025 | |
Approximation of optimal feedback controls for stochastic reaction-diffusion equations
Technische Universität Berlin, Straße des 17. Juni 135, Berlin, Germany
* Corresponding author: alexander_vogler@hotmail.de
Received:
29
August
2023
Accepted:
6
November
2024
In this paper, we present a method to approximate optimal feedback controls for stochastic reaction-diffusion equations. We derive two approximation results providing the theoretical foundation of our approach and allowing for explicit error estimates. The approximation of optimal feedback controls by neural networks is discussed as an explicit application of our method. We illustrate our findings in the case of a linear quadratic control problem with a numerical example.
Mathematics Subject Classification: 93E20 / 93B52 / 60H15 / 65K10
Key words: Stochastic optimal control / reaction-diffusion equations / adjoint calculus / variational methods / artificial neural networks
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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