Vector-valued multibang control of differential equations

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 $\mathcal{M}\subset {\mathbb{R}}^m$. After convex relaxation, one obtains a well-posed optimization problem, which still promotes control values in $\mathcal{M}$. 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.

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• Efficient high-resolution RF pulse design applied to simultaneous multi-slice excitation
• A convex analysis approach to multi-material topology optimization
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Cited by in corpus (3)

• Parabolic optimal control problems with combinatorial switching constraints -- Part I: Convex relaxations
• Parabolic optimal control problems with combinatorial switching constraints -- Part II: Outer approximation algorithm
• Error estimates for the approximation of multibang control problems