# Simultaneous controllability in sharp time for two elastic strings

Sergei Avdonin; Marius Tucsnak

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

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

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topAvdonin, Sergei, and Tucsnak, Marius. "Simultaneous controllability in sharp time for two elastic strings." ESAIM: Control, Optimisation and Calculus of Variations 6 (2001): 259-273. <http://eudml.org/doc/90594>.

@article{Avdonin2001,

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 reachable space},

language = {eng},

pages = {259-273},

publisher = {EDP-Sciences},

title = {Simultaneous controllability in sharp time for two elastic strings},

url = {http://eudml.org/doc/90594},

volume = {6},

year = {2001},

}

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

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 reachable space

UR - http://eudml.org/doc/90594

ER -

## References

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