Minimization of the L p -Norm, p ≥ 1 of Dirichlet-Type Boundary Controls for the 1D Wave Equation

Smirnov, Ilya; Dmitrieva, Anastasia

doi:10.1007/978-3-319-66616-7_6

Minimization of the L _p-Norm, p ≥ 1 of Dirichlet-Type Boundary Controls for the 1D Wave Equation

Ilya Smirnov³ &
Anastasia Dmitrieva³

Conference paper
First Online: 01 November 2017

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 213))

Abstract

This paper provides a modified method that allows one to solve the problem of the optimal boundary controls μ(t) and ν(t) of displacements at two ends of a string for a large time interval T = 2ln, where n = 1, 2, 3, … It should be noted that the minimization was made in the space L _p with p ≥ 1. Besides, it was found that the derivatives of above-mentioned functions are 2l-periodic functions.

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References

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Acknowledgements

The work was supported by the grant MK − 3400. 2017. 1.

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Authors and Affiliations

Lomonosov Moscow State University, Moscow, Russia
Ilya Smirnov & Anastasia Dmitrieva

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Ilya Smirnov
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Anastasia Dmitrieva
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Correspondence to Ilya Smirnov .

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Editors and Affiliations

Industrial and Systems Engineering Department, Lehigh University, Bethlehem, Pennsylvania, USA
Martin Takáč
Industrial and Systems Engineering Department, Lehigh University, Bethlehem, Pennsylvania, USA
Tamás Terlaky

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Smirnov, I., Dmitrieva, A. (2017). Minimization of the L _p-Norm, p ≥ 1 of Dirichlet-Type Boundary Controls for the 1D Wave Equation. In: Takáč, M., Terlaky, T. (eds) Modeling and Optimization: Theory and Applications. MOPTA 2016. Springer Proceedings in Mathematics & Statistics, vol 213. Springer, Cham. https://doi.org/10.1007/978-3-319-66616-7_6

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DOI: https://doi.org/10.1007/978-3-319-66616-7_6
Published: 01 November 2017
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-66615-0
Online ISBN: 978-3-319-66616-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)

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