Vector-Valued Multibang Control of Differential Equations

DOI10.1137/16M1104998zbMATH Open1393.49007arXiv1611.07853OpenAlexW3101287369WikidataQ129633322 ScholiaQ129633322MaRDI QIDQ4569277

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Publication date: 28 June 2018

Published in: (Search for Journal in Brave)

Abstract: We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to pointwise take values in a finite set $mathcalMsubsetmathbb{R}^m$. After convex relaxation, one obtains a well-posed optimization problem, which still promotes control values in $mathcalM$. We state the corresponding well-posedness and stability analysis and exemplify the results for two specific cases of quite general interest, optimal control of the Bloch equation and optimal control of an elastic deformation. We finally formulate a semismooth Newton method to numerically solve a regularized version of the optimal control problem and illustrate the behavior of the approach for our example cases.

Full work available at URL: https://arxiv.org/abs/1611.07853

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