Exact boundary controllability of a hybrid system of elasticity by the HUM method

Bopeng Rao

ESAIM: Control, Optimisation and Calculus of Variations (2001)

  • Volume: 6, page 183-199
  • ISSN: 1292-8119

Abstract

top
We consider the exact controllability of a hybrid system consisting of an elastic beam, clamped at one end and attached at the other end to a rigid antenna. Such a system is governed by one partial differential equation and two ordinary differential equations. Using the HUM method, we prove that the hybrid system is exactly controllable in an arbitrarily short time in the usual energy space.

How to cite

top

Rao, Bopeng. "Exact boundary controllability of a hybrid system of elasticity by the HUM method." ESAIM: Control, Optimisation and Calculus of Variations 6 (2001): 183-199. <http://eudml.org/doc/90588>.

@article{Rao2001,
abstract = {We consider the exact controllability of a hybrid system consisting of an elastic beam, clamped at one end and attached at the other end to a rigid antenna. Such a system is governed by one partial differential equation and two ordinary differential equations. Using the HUM method, we prove that the hybrid system is exactly controllable in an arbitrarily short time in the usual energy space.},
author = {Rao, Bopeng},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {hybrid system; weak solution; exact controllability; singular control; unique continuation; exact boundary controllability; elastic beam; coupled system},
language = {eng},
pages = {183-199},
publisher = {EDP-Sciences},
title = {Exact boundary controllability of a hybrid system of elasticity by the HUM method},
url = {http://eudml.org/doc/90588},
volume = {6},
year = {2001},
}

TY - JOUR
AU - Rao, Bopeng
TI - Exact boundary controllability of a hybrid system of elasticity by the HUM method
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2001
PB - EDP-Sciences
VL - 6
SP - 183
EP - 199
AB - We consider the exact controllability of a hybrid system consisting of an elastic beam, clamped at one end and attached at the other end to a rigid antenna. Such a system is governed by one partial differential equation and two ordinary differential equations. Using the HUM method, we prove that the hybrid system is exactly controllable in an arbitrarily short time in the usual energy space.
LA - eng
KW - hybrid system; weak solution; exact controllability; singular control; unique continuation; exact boundary controllability; elastic beam; coupled system
UR - http://eudml.org/doc/90588
ER -

References

top
  1. [1] C. Castro and E. Zuazua, Boundary controllability of a hybrid system consisting in two flexible beams connected by a point mass. SIAM J. Control Optim. 36 (1998) 1576–1595. Zbl0909.35085
  2. [2] S. Hanssen and E. Zuazua, Exact controllability and stabilization of a vibration string with an interior point mass. SIAM J. Control Optim. 33 (1995) 1357–1391. Zbl0853.93018
  3. [3] W. Littman and L. Markus, Exact boundary controllability of a hybrid system of elasticity. Arch. Rational Mech. Anal. 103 (1988) 193–236. Zbl0656.73029
  4. [4] W. Littman and L. Markus, Stabilization of a hybrid system of elasticity by feedback boundary damping. Ann. Mat. Pura Appl. 152 (1988) 281–330. Zbl0664.73025
  5. [5] J.L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Vol. I. Masson, Paris (1988). Zbl0653.93003
  6. [6] J.L. Lions, Exact controllability, stabilizability, and perturbations for distributed systems. SIAM Rev. 30 (1988) 1–68. Zbl0644.49028
  7. [7] L. Markus and Y.C. You, Dynamical boundary control for elastic Al plates of general shape. SIAM J. Control Optim. 31 (1993) 983–992. Zbl0785.93026
  8. [8] S. Micu and E. Zuazua, Boundary controllability of a linear hybrid system arising in the control noise. SIAM J. Control Optim. 35 (1987) 1614–1637. Zbl0888.35017
  9. [9] A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York (1983). Zbl0516.47023MR710486
  10. [10] B. Rao, Stabilisation du modèle SCOLE par un contrôle frontière a priori borné. C. R. Acad. Sci. Paris Sér. I Math. 316 (1993) 1061–1066. Zbl0797.49007
  11. [11] B. Rao, Uniform stabilization and exact controllability of Kirchhoff plates with dynamical boundary controls. 
  12. [12] B. Rao, Uniform stabilization of a hybrid system of elasticity. SIAM J. Control Optim. 33 (1995) 440–454. Zbl0821.93041
  13. [13] B. Rao, Contrôlabilité exacte frontière d’un système hybride en élasticité par la méthode HUM. C. R. Acad. Sci. Paris Sér. I Math. 324 (1997) 889–894. Zbl0894.93006
  14. [14] J. Simon, Compact sets in the space L p ( 0 , T ; B ) . Ann. Mat. Pura Appl. (IV) CXLVI (1987) 65–96. Zbl0629.46031
  15. [15] M. Slemrod, Feedback stabilization of a linear system in Hilbert space with an a priori bounded control. Math. Control Signals Systems (1989) 265–285. Zbl0676.93057
  16. [16] E. Zuazua, Contrôlabilité exacte en un temps arbitrairement petit de quelques modèles de plaques, in Lions [5], 465–491. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.