Agnes Lamacz (Uni Duisburg-Essen): High-order homogenization in optimal control by the Bloch wave method

Wednesday, 01.06.2022 14:00 im Raum M5

Mathematik und Informatik

In this talk we examine a linear-quadratic optimal control problem in which the cost functional and the elliptic state equation involve a highly oscillatory periodic coefficient $A^\varepsilon$. The small parameter $\varepsilon>0$ denotes the periodicity length. We propose a high-order effective control problem with constant coefficients and prove a corrector result which allows to approximate the original optimal solution with error $O(\varepsilon^M)$, where $M\in\mathbb{N}$ is as large as one likes. Our analysis relies on a Bloch wave expansion of the optimal solution and is performed in two steps. In the first step, we expand the lowest Bloch eigenvalue in a Taylor series to obtain a high-order effective optimal control problem. In the second step, the original and the effective problem are rewritten in terms of the Bloch and the Fourier transform, respectively. This allows for a direct comparison of the optimal solutions via the corresponding variational inequalities.

Angelegt am Wednesday, 11.05.2022 13:50 von cauri_01
Geändert am Tuesday, 31.05.2022 09:02 von cauri_01
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