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Optimal shape and position of the support for the internal exact control of a string. (English) Zbl 1155.49312
Summary: We consider the problem of optimizing the shape and position of the support $\omega$ of the internal exact control of minimal ${L}^{2}\left(0,T;{L}^{2}\left(\omega \right)\right)$-norm for the 1-D wave equation. A relaxation for this problem is found and the minimizers of the relaxed problem are characterized through first-order optimality conditions.
##### MSC:
 49Q20 Variational problems in a geometric measure-theoretic setting 93B05 Controllability 70Q05 Control of mechanical systems (general mechanics) 74K05 Strings (solid mechanics)
##### References:
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