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Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons

Published online by Cambridge University Press:  15 August 2002

Mikhail Belishev  and
Aleksandr Glasman
Mikhail Belishev
Affiliation:
Saint-Petersburg Department of Steklov Mathematical Institute, Fontanka 27, Saint-Petersburg 191011, Russia; belishev@bel.pdmi.ras.ru. Supported by RFBR, grant 98-01-00314.
Aleksandr Glasman
Affiliation:
Saint-Petersburg State University, Saint-Petersburg, Russia. Supported by RFBR, grant 99-01-00107.
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Abstract

The paper deals with a boundary control problem for the Maxwell dynamical system in a bounbed domain Ω ⊂ R3. Let ΩT ⊂ Ω be the subdomain filled by waves at the moment T, T* the moment at which the waves fill the whole of Ω. The following effect occurs: for small enough T the system is approximately controllable in ΩT whereas for larger T < T* a lack of controllability is possible. The subspace of unreachable states is of finite dimension determined by topological characteristics of ΩT.

Keywords

Maxwell's dynamical systemboundary controlunreachable statestopology of a domain.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 207 - 217
Copyright
© EDP Sciences, SMAI, 2000

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