Controllability of a Nonhomogeneous String and Ring under Time Dependent Tension

S. A. Avdonin; B. P. Belinskiy; L. Pandolfi

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 4, page 4-31
  • ISSN: 0973-5348

Abstract

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We study controllability for a nonhomogeneous string and ring under an axial stretching tension that varies with time. We consider the boundary control for a string and distributed control for a ring. For a string, we are looking for a control f(t) ∈ L2(0, T) that drives the state solution to rest. We show that for a ring, two forces are required to achieve controllability. The controllability problem is reduced to a moment problem for the control. We describe the set of initial data which may be driven to rest by the control. The proof is based on an auxiliary basis property result.

How to cite

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Avdonin, S. A., Belinskiy, B. P., and Pandolfi, L.. "Controllability of a Nonhomogeneous String and Ring under Time Dependent Tension." Mathematical Modelling of Natural Phenomena 5.4 (2010): 4-31. <http://eudml.org/doc/197684>.

@article{Avdonin2010,
abstract = {We study controllability for a nonhomogeneous string and ring under an axial stretching tension that varies with time. We consider the boundary control for a string and distributed control for a ring. For a string, we are looking for a control f(t) ∈ L2(0, T) that drives the state solution to rest. We show that for a ring, two forces are required to achieve controllability. The controllability problem is reduced to a moment problem for the control. We describe the set of initial data which may be driven to rest by the control. The proof is based on an auxiliary basis property result.},
author = {Avdonin, S. A., Belinskiy, B. P., Pandolfi, L.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {string equation; ring equation; exact controllability; Riesz basis; moment problem},
language = {eng},
month = {5},
number = {4},
pages = {4-31},
publisher = {EDP Sciences},
title = {Controllability of a Nonhomogeneous String and Ring under Time Dependent Tension},
url = {http://eudml.org/doc/197684},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Avdonin, S. A.
AU - Belinskiy, B. P.
AU - Pandolfi, L.
TI - Controllability of a Nonhomogeneous String and Ring under Time Dependent Tension
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/5//
PB - EDP Sciences
VL - 5
IS - 4
SP - 4
EP - 31
AB - We study controllability for a nonhomogeneous string and ring under an axial stretching tension that varies with time. We consider the boundary control for a string and distributed control for a ring. For a string, we are looking for a control f(t) ∈ L2(0, T) that drives the state solution to rest. We show that for a ring, two forces are required to achieve controllability. The controllability problem is reduced to a moment problem for the control. We describe the set of initial data which may be driven to rest by the control. The proof is based on an auxiliary basis property result.
LA - eng
KW - string equation; ring equation; exact controllability; Riesz basis; moment problem
UR - http://eudml.org/doc/197684
ER -

References

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