Controllability of a string under tension

Pages: 57 - 67, Issue Special, July 2003

 Abstract        Full Text (187.8K)              

Sergei A. Avdonin - University of Alaska Fairbanks, Fairbanks, AK 99775-6660, United States (email)
Boris P. Belinskiy - Department of Mathematics, University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403-2598, United States (email)

Abstract: We study controllability for a string under an axial stretching tension. The tension is a sum of a constant positive term and a small, slowly variable, load. We are looking for an exterior force $g(x)f(t)$ that drives the state solution to rest. The controllability problem is reduced to a moment problem for the control $f(t)$: We describe the set of initial data which may be driven to rest by a control $f(t) \in L^2(0, T)$: The description is obtained in terms of the Fourier coefficients of the initial data. The proof is based on an auxiliary basis property result.

Keywords:  string equation, exact controllability, Riesz basis, moment problem.
Mathematics Subject Classification:  Primary: 93B05, 35C20, 35L20; Secondary: 93C20.

Received: September 2002;      Revised: March 2003;      Published: April 2003.