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unreachable states

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons
Mikhail Belishev, Aleksandr Glasman
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 5 / 2000

Published online by Cambridge University Press:

15 August 2002, pp. 207-217

Print publication:

2000
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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.