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• W3091914877 abstract "This article examines a linear-quadratic elliptic optimal control problem in which the cost functional and the 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 that provides an approximation of the original one with error $O(varepsilon^M)$, where $Minmathbb{N}$ 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 control problems via the corresponding variational inequalities." @default.
• W3091914877 created "2020-10-15" @default.
• W3091914877 creator A5000672190 @default.
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• W3091914877 date "2020-10-09" @default.
• W3091914877 modified "2023-09-27" @default.
• W3091914877 title "High-order homogenization in optimal control by the Bloch wave method" @default.
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