The Kalman condition for the boundary controllability of coupled 1-d wave equations

Sergei Avdonin; Jeff Park; Luz de Teresa

doi:10.3934/eect.2020005

Article Contents

2020, Volume 9, Issue 1: 255-273. Doi: 10.3934/eect.2020005

This issue Previous Article Multi-valued perturbation to evolution problems involving time dependent maximal monotone operators Next Article Stability analysis in some strongly prestressed rectangular plates

The Kalman condition for the boundary controllability of coupled 1-d wave equations

1.
Dept. of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775, USA
2.
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, G. U. 04510 D.F., México

Received: December 2018

Revised: March 2019

Early access: August 2019

Published: March 2020

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Abstract

The focus of this paper is the exact controllability of a system of $ N $ one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We give a Kalman condition (necessary and sufficient) and give a description of the attainable set. In general, this set is not optimal, but can be refined under certain conditions.

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Mathematics Subject Classification: Primary: 35Q93, 93B05; Secondary: 35L05, 15A18.

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References

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