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Zbl 1155.49312
Periago, Francisco
Optimal shape and position of the support for the internal exact control of a string.
(English)
[J] Syst. Control Lett. 58, No. 2, 136-140 (2009). ISSN 0167-6911

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 2000:
*49Q20 Variational problems in geometric measure-theoretic setting
93B05 Controllability
70Q05 Control of mechanical systems
74K05 Strings

Keywords: optimal shape design; exact controllability; wave equation; relaxation; optimality conditions

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