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Simultaneous controllability in sharp time for two elastic strings

Published online by Cambridge University Press:  15 August 2002

Sergei Avdonin  and
Marius Tucsnak
Sergei Avdonin
Affiliation:
Department of Applied Mathematics and Control, St. Petersburg State University, St. Petersburg 198904, Russia. Department of Mathematics and Statistics, The Flinders University of South Australia, P.O. Box 2100, Adelaide 5001, Australia; [email protected].
Marius Tucsnak
Affiliation:
Department of Mathematics, University of Nancy-I, BP. 239, 54506 Vandœuvre-lès-Nancy, France; [email protected].
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Abstract

We study the simultaneously reachable subspace for two strings controlled from a common endpoint. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability. Moreover we prove the lack of simultaneous exact controllability and we study the space of simultaneously reachable states as a function of the position of the joint. For each type of controllability result we give the sharp controllability time.

Keywords

Exact controllabilityspectral controllabilityapproximate controllabilitysimultaneous controllabilitystring equationboundary controlRiesz basis.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 259 - 273
Copyright
© EDP Sciences, SMAI, 2001

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