Boundary control of the Maxwell dynamical system: lack of controllability by topological reasons
Saint-Petersburg Department of Steklov Mathematical
Institute, Fontanka 27, Saint-Petersburg 191011, Russia; email@example.com.
Supported by RFBR, grant 98-01-00314.
2 Saint-Petersburg State University, Saint-Petersburg, Russia. Supported by RFBR, grant 99-01-00107.
Revised: 30 December 1999
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.
Mathematics Subject Classification: 93B05 / 35B37 / 35Q60 / 78A25 / 93C20
Key words: Maxwell's dynamical system / boundary control / unreachable states / topology of a domain.
© EDP Sciences, SMAI, 2000