Controlling a non-homogeneous Timoshenko beam with the aid of the torque

Grigory M. Sklyar; Grzegorz Szkibiel

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 3, page 587-598
  • ISSN: 1641-876X

Abstract

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Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally the appropriate form and the results on C⁰-continuous semigroups may be applied.

How to cite

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Grigory M. Sklyar, and Grzegorz Szkibiel. "Controlling a non-homogeneous Timoshenko beam with the aid of the torque." International Journal of Applied Mathematics and Computer Science 23.3 (2013): 587-598. <http://eudml.org/doc/262353>.

@article{GrigoryM2013,
abstract = {Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally the appropriate form and the results on C⁰-continuous semigroups may be applied.},
author = {Grigory M. Sklyar, Grzegorz Szkibiel},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Timoshenko beam; rotating beam control; approximate control; stabilizability},
language = {eng},
number = {3},
pages = {587-598},
title = {Controlling a non-homogeneous Timoshenko beam with the aid of the torque},
url = {http://eudml.org/doc/262353},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Grigory M. Sklyar
AU - Grzegorz Szkibiel
TI - Controlling a non-homogeneous Timoshenko beam with the aid of the torque
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 3
SP - 587
EP - 598
AB - Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally the appropriate form and the results on C⁰-continuous semigroups may be applied.
LA - eng
KW - Timoshenko beam; rotating beam control; approximate control; stabilizability
UR - http://eudml.org/doc/262353
ER -

References

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  4. Kato, T. (1966). Perturbation Theory for Linear Operators, Springer-Verlag, Berlin. Zbl0148.12601
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  11. Sklyar, G.M. and Rezounenko, A.V. (2003). Strong asymptotic stability and constructing of stabilizing control, Matematitcheskaja Fizika, Analiz i Geometria 10(4): 569-582. Zbl1066.93047
  12. Sklyar, G.M. and Szkibiel, G. (2007). Spectral properties of non-homogeneous Timoshenko beam and its controllability, Mekhanika Tverdogo Tela (37): 175-183. Zbl1131.74034
  13. Sklyar, G.M. and Szkibiel, G. (2008a). Controllability from rest to arbitrary position of non-homogeneous Timoshenko beam, Matematitcheskij Analiz i Geometria 4(2): 305-318. Zbl1170.93011
  14. Sklyar, G.M. and Szkibiel, G. (2008b). Spectral properties of non-homogeneous Timoshenko beam and its rest to rest controllability, Journal of Mathematical Analysis and Applications (338): 1054-1069. Zbl1131.74034
  15. Sklyar, G.M. and Szkibiel, G. (2012). Approximation of extremal solution of non-Fourier moment problem and optimal control for non-homogeneous vibrating systems, Journal of Mathematical Analysis and Applications (387): 241-250. Zbl1231.49029
  16. Zerrik, E., Larhrissi, R. and Bourray, H. (2007). An output controllability problem for semilinear distributed hyperbolic systems, International Journal of Applied Mathematics Computer Science 17(4): 437-448, DOI: 10.2478/v10006-007-0035-y. Zbl1234.93023

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