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.
Keywords: exact controllability, spectral controllability, approximate controllability, simultaneous controllability, string equation, boundary control, Riesz basis
@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},
zbl = {0995.93036},
mrnumber = {1816075},
language = {en},
url = {http://archive.numdam.org/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 DA - 2001/// SP - 259 EP - 273 VL - 6 PB - EDP-Sciences UR - http://archive.numdam.org/item/COCV_2001__6__259_0/ UR - https://zbmath.org/?q=an%3A0995.93036 UR - https://www.ams.org/mathscinet-getitem?mr=1816075 LA - en ID - COCV_2001__6__259_0 ER -
Avdonin, Sergei; Tucsnak, Marius. Simultaneous controllability in sharp time for two elastic strings. ESAIM: Control, Optimisation and Calculus of Variations, Volume 6 (2001), pp. 259-273. http://archive.numdam.org/item/COCV_2001__6__259_0/
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