Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin; Marius Tucsnak

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

  • Volume: 6, page 259-273
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Avdonin, Sergei, and Tucsnak, Marius. "Simultaneous controllability in sharp time for two elastic strings." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 259-273. <http://eudml.org/doc/197323>.

@article{Avdonin2010,
abstract = { 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. },
author = {Avdonin, Sergei, Tucsnak, Marius},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Exact controllability; spectral controllability; approximate controllability; simultaneous controllability; string equation; boundary control; Riesz basis.; simultaneous controllability; Riesz basis; simultaneous reachable space},
language = {eng},
month = {3},
pages = {259-273},
publisher = {EDP Sciences},
title = {Simultaneous controllability in sharp time for two elastic strings},
url = {http://eudml.org/doc/197323},
volume = {6},
year = {2010},
}

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
DA - 2010/3//
PB - EDP Sciences
VL - 6
SP - 259
EP - 273
AB - 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.
LA - eng
KW - Exact controllability; spectral controllability; approximate controllability; simultaneous controllability; string equation; boundary control; Riesz basis.; simultaneous controllability; Riesz basis; simultaneous reachable space
UR - http://eudml.org/doc/197323
ER -

References

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