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

Mikhail Belishev; Aleksandr Glasman

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 5, page 207-217
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Belishev, Mikhail, and Glasman, Aleksandr. "Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons." ESAIM: Control, Optimisation and Calculus of Variations 5 (2010): 207-217. <http://eudml.org/doc/197267>.

@article{Belishev2010,
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. },
author = {Belishev, Mikhail, Glasman, Aleksandr},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Maxwell's dynamical system; boundary control; unreachable states; topology of a domain.; topology of a domain},
language = {eng},
month = {3},
pages = {207-217},
publisher = {EDP Sciences},
title = {Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons},
url = {http://eudml.org/doc/197267},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Belishev, Mikhail
AU - Glasman, Aleksandr
TI - Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 5
SP - 207
EP - 217
AB - 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.
LA - eng
KW - Maxwell's dynamical system; boundary control; unreachable states; topology of a domain.; topology of a domain
UR - http://eudml.org/doc/197267
ER -

References

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