On controllability of a linear elastic beam with memory under longitudinal load

Sergei A. Avdonin; Boris P. Belinskiy

doi:10.3934/eect.2014.3.231

Article Contents

2014, Volume 3, Issue 2: 231-245. Doi: 10.3934/eect.2014.3.231

This issue Previous Article Stability and stabilization of infinite-dimensional linear port-Hamiltonian systems Next Article Non-smooth unobservable states in control problem for the wave equation in $\mathbb{R}^3$

On controllability of a linear elastic beam with memory under longitudinal load

Sergei A. Avdonin^1, and
Boris P. Belinskiy^2,

1.
University of Alaska Fairbanks, Fairbanks, AK 99775-6660
2.
University of Tennessee at Chattanooga, 615 McCallie Avenue, Chattanooga, TN 37403-2598

Received: December 31, 2012

Revised: February 28, 2014

Published: May 2014

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Abstract

This work is motivated by the control problem for a linear elastic beam under a longitudinal load when the material of the beam has memory. We reduce the problem of controllability to a nonstandard moment problem. The solution of the latter problem is based on the Riesz basis property for a family of functions quadratically close to the nonharmonic exponentials. This result requires the detailed analysis of an integro--differential equation, and is of interest in itself for Function Theory.

Keywords:

Control for distributed parameter systems,
viscoelastic beam,
memory,
moment problem,
bases of functions,
nonharmonic exponentials,
Sobolev spaces.

Mathematics Subject Classification: Primary: 34H05, 93B05, 93C20; Secondary: 74Dxx, 35Q93, 46E35, 34B09, 35Pxx, 42A70.

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