Stabilisation d'une poutre. Étude du taux optimal de décroissance de l'énergie élastique

Francis Conrad; Fatima-Zahra Saouri

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 7, page 567-595
  • ISSN: 1292-8119

Abstract

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We study the stability of a flexible beam clamped at one end. A mass is attached at the other end, where a control moment is applied. The boundary control is proportional to the angular velocity at the end. By spectral analysis, we prove that the optimal decay rate of the energy is given by the spectrum of the generator of the semigroup associated to the system.

How to cite

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Conrad, Francis, and Saouri, Fatima-Zahra. "Stabilisation d'une poutre. Étude du taux optimal de décroissance de l'énergie élastique." ESAIM: Control, Optimisation and Calculus of Variations 7 (2010): 567-595. <http://eudml.org/doc/90635>.

@article{Conrad2010,
abstract = { We study the stability of a flexible beam clamped at one end. A mass is attached at the other end, where a control moment is applied. The boundary control is proportional to the angular velocity at the end. By spectral analysis, we prove that the optimal decay rate of the energy is given by the spectrum of the generator of the semigroup associated to the system. },
author = {Conrad, Francis, Saouri, Fatima-Zahra},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Équation des poutres; contrôle frontière; stabilisation uniforme; analyse spectrale.; spectral analysis; spectrum of the generator of the semigroup},
language = {eng},
month = {3},
pages = {567-595},
publisher = {EDP Sciences},
title = {Stabilisation d'une poutre. Étude du taux optimal de décroissance de l'énergie élastique},
url = {http://eudml.org/doc/90635},
volume = {7},
year = {2010},
}

TY - JOUR
AU - Conrad, Francis
AU - Saouri, Fatima-Zahra
TI - Stabilisation d'une poutre. Étude du taux optimal de décroissance de l'énergie élastique
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 7
SP - 567
EP - 595
AB - We study the stability of a flexible beam clamped at one end. A mass is attached at the other end, where a control moment is applied. The boundary control is proportional to the angular velocity at the end. By spectral analysis, we prove that the optimal decay rate of the energy is given by the spectrum of the generator of the semigroup associated to the system.
LA - eng
KW - Équation des poutres; contrôle frontière; stabilisation uniforme; analyse spectrale.; spectral analysis; spectrum of the generator of the semigroup
UR - http://eudml.org/doc/90635
ER -

References

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  10. H. Laousy, Sur quelques problèmes de stabilisation de systèmes à paramètres distribués. Thèse de l'Université de Metz (1997).  
  11. H. Laousy et B. Chentouf, On the boundary stabilization of a hybrid system, dans 14 t h IFAC World Congress (1999).  
  12. W. Littman et L. Markus, Stabilization of a hybrid system of elasticity by feedback boundary damping. Ann. Mat. Pura Appl.152 (1988) 281-330.  Zbl0664.73025
  13. B. Rao, Uniform stabilization of a hybrid system of elasticity. SIAM J. Control Optim.33 (1995) 440-454.  Zbl0821.93041
  14. P. Rideau, Contrôle d'un assemblage de poutres flexibles par des capteurs-actionneurs ponctuels : étude du spectre du système, Thèse. École Nationale Supérieure des Mines de Paris, Sophia-Antipolis (1995).  
  15. D.L. Russell, Decay rates for weakly damped systems in Hilbert space obtained with control-theoretic methods. J. Differential Equations19 (1975) 344-370.  Zbl0326.93018
  16. F.Z. Saouri, Stabilisation d'une poutre avec contrôle force. Étude du taux optimal de décroissance de l'énergie élastique. Prépublication de l'Institut Elie Cartan, No. 47 (1997).  
  17. A. Shkalikov, Boundary problems for ordinary differential equations with parameter in the boundary conditions. J. Soviet Math.33 (1986) 1311-1342.  Zbl0609.34019

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