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.
MSC:
| 49Q20 | Variational problems in a geometric measure-theoretic setting |
| 93B05 | Controllability |
| 70Q05 | Control of mechanical systems |
| 74K05 | Strings |
Keywords:
optimal shape design; exact controllability; wave equation; relaxation; optimality conditionsReferences:
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