On the Solvability of Trigonometric Moment Problems Arising in the Problem of Controllability of Rotating Beams

Korobov, V. I.; Krabs, W.; Sklyar, G. M.

doi:10.1007/978-3-0348-8148-7_12

On the Solvability of Trigonometric Moment Problems Arising in the Problem of Controllability of Rotating Beams

V. I. Korobov^9,10,
W. Krabs¹¹ &
G. M. Sklyar^12,13

Conference paper

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 139))

Abstract

In this paper the problem of controllability of a slowly rotating Timoshenko beam in a horizontal plane from the position of rest into an arbitrary position at some given time is investigated. It is solved with the aid of a theorem by D. Ullrich on a trigonometric moment problem which generalizes a classical result of Paley and Wiener.

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References

C. Castro and E. Zŭazŭa, Boundary Controllability of a Hybrid System Consisting in Two Fuxible Beams Connected by a Point Mass. SIAM J. Control Optim. 36(1998), 1576–1595.
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R.E.A.C. Paley and N. Wiener, Fourier Transforms in the Complex Domain. Amer. Math. Soc., Providence, R.J., 1934; 3rd printing 1978.
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D Ullrich, Divided Differences and Systems of Norharmonic Fourier Series. Proc. Amer. Soc. 80(1980), 47–57.
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Authors and Affiliations

Inst. Math. Univ., ul. Wielkopolska 15, Szczecin, 70-451, Poland
V. I. Korobov
Dept. Diff. Equat. and Control, Kharkov National University, Svoboda sqr.4, Kharkov, 61077, Ukraine
V. I. Korobov
Department of Mathematics, Technical University of Darmstadt, Schlossgartenstrasse 7, Darmstadt, 64289, Germany
W. Krabs
Inst. Math. Univ., ul. Wielkopolska 15, Szczecin, 70-451, Poland
G. M. Sklyar
Dept. Math. Anal., Kharkov National University, Svoboda sqr.4, Kharkov, 61077, Ukraine
G. M. Sklyar

Authors

V. I. Korobov
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W. Krabs
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G. M. Sklyar
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Editors and Affiliations

Fachbereich Mathematik, Arbeitsgruppe 10, Technische Universität Darmstadt, Schlossgartenstrasse 7, 64289, Darmstadt, Germany
Günter Leugering

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Korobov, V.I., Krabs, W., Sklyar, G.M. (2001). On the Solvability of Trigonometric Moment Problems Arising in the Problem of Controllability of Rotating Beams. In: Hoffmann, KH., Lasiecka, I., Leugering, G., Sprekels, J., Tröltzsch, F. (eds) Optimal Control of Complex Structures. ISNM International Series of Numerical Mathematics, vol 139. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8148-7_12

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DOI: https://doi.org/10.1007/978-3-0348-8148-7_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9456-2
Online ISBN: 978-3-0348-8148-7
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