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Controllability of a Nonhomogeneous String and Ring under TimeDependent Tension

Published online by Cambridge University Press:  12 May 2010

S. A. Avdonin ,
B. P. Belinskiy  and
L. Pandolfi
S. A. Avdonin*
Affiliation:
University of Alaska Fairbanks, Fairbanks, AK 99775-6660, USA
B. P. Belinskiy
Affiliation:
University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403-2598, USA
L. Pandolfi
Affiliation:
Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
*
* Corresponding author. E-mail:ffsaa@uaf.edu
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Abstract

We study controllability for a nonhomogeneous string and ring under an axial stretchingtension that varies with time. We consider the boundary control for a string anddistributed control for a ring. For a string, we are looking for a controlf(t) ∈ L 2(0,T) that drives the state solution to rest. We show that for a ring, two forcesare required to achieve controllability. The controllability problem is reduced to amoment problem for the control. We describe the set of initial data which may be driven torest by the control. The proof is based on an auxiliary basis property result.

Keywords

string equationring equationexact controllabilityRiesz basismoment problem
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 4: Spectral problems. Issue dedicated to the memory of M. Birman , 2010 , pp. 4 - 31
Copyright
© EDP Sciences, 2010

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