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We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.
@article{COCV_2001__6__259_0,
author = {Avdonin, Sergei and Tucsnak, Marius},
title = {Simultaneous controllability in sharp time for two elastic strings},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {259--273},
publisher = {EDP-Sciences},
volume = {6},
year = {2001},
mrnumber = {1816075},
zbl = {0995.93036},
language = {en},
url = {http://geodesic.mathdoc.fr/item/COCV_2001__6__259_0/}
}
TY - JOUR AU - Avdonin, Sergei AU - Tucsnak, Marius TI - Simultaneous controllability in sharp time for two elastic strings JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2001 SP - 259 EP - 273 VL - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/item/COCV_2001__6__259_0/ LA - en ID - COCV_2001__6__259_0 ER -
%0 Journal Article %A Avdonin, Sergei %A Tucsnak, Marius %T Simultaneous controllability in sharp time for two elastic strings %J ESAIM: Control, Optimisation and Calculus of Variations %D 2001 %P 259-273 %V 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/item/COCV_2001__6__259_0/ %G en %F COCV_2001__6__259_0
Avdonin, Sergei; Tucsnak, Marius. Simultaneous controllability in sharp time for two elastic strings. ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 259-273. http://geodesic.mathdoc.fr/item/COCV_2001__6__259_0/