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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 $L^{2}(0,T;L^{2}(\omega ))$-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.

49Q20Variational problems in a geometric measure-theoretic setting
70Q05Control of mechanical systems (general mechanics)
74K05Strings (solid mechanics)
Full Text: DOI
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