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We consider a controllability problem for a beam, clamped at one boundary and free at the other boundary, with an attached piezoelectric actuator. By Hilbert Uniqueness Method (HUM) and new results on diophantine approximations, we prove that the space of exactly initial controllable data depends on the location of the actuator. We also illustrate these results with numerical simulations.
@article{COCV_2006__12_3_545_0,
author = {Cr\'epeau, Emmanuelle and Prieur, Christophe},
title = {Control of a clamped-free beam by a piezoelectric actuator},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {545--563},
publisher = {EDP-Sciences},
volume = {12},
number = {3},
year = {2006},
doi = {10.1051/cocv:2006008},
mrnumber = {2224825},
zbl = {1106.93008},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006008/}
}
TY - JOUR AU - Crépeau, Emmanuelle AU - Prieur, Christophe TI - Control of a clamped-free beam by a piezoelectric actuator JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 545 EP - 563 VL - 12 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006008/ DO - 10.1051/cocv:2006008 LA - en ID - COCV_2006__12_3_545_0 ER -
%0 Journal Article %A Crépeau, Emmanuelle %A Prieur, Christophe %T Control of a clamped-free beam by a piezoelectric actuator %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 545-563 %V 12 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006008/ %R 10.1051/cocv:2006008 %G en %F COCV_2006__12_3_545_0
Crépeau, Emmanuelle; Prieur, Christophe. Control of a clamped-free beam by a piezoelectric actuator. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 545-563. doi: 10.1051/cocv:2006008
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