Issue |
ESAIM: COCV
Volume 4, 1999
|
|
---|---|---|
Page(s) | 405 - 418 | |
DOI | https://doi.org/10.1051/cocv:1999115 | |
Published online | 15 August 2002 |
Control Norms for Large Control Times
Russian Center of Laser Physics, St. Petersburg University,
Ul'yanovskaya ul. 1, Petrodvorets, St. Petersburg 198904,
Russia; Sergei.Ivanov@pobox.spbu.ru.
Received:
7
September
1998
Revised:
12
March
1999
A control system of the second order in time with control is considered. If the system is controllable in a strong sense and uT is the control steering the system to the rest at time T, then the L2–norm of uT decreases as while the –norm of uT is approximately constant. The proof is based on the moment approach and properties of the relevant exponential family. Results are applied to the wave equation with boundary or distributed controls.
Résumé
On considère un système du second ordre à contrôler en temps avec une fonction . Si le système est contrôlable au sens fort et uT est la fonction de contrôle qui gouverne le système à partir du temps T, alors la norme L2 de uT décroît comme tandis que sa norme est approximativement constante. La preuve est basée sur la théorie des moments et les propriétés d'une famille approprièe d'exponentielles. Ces résultats sont ensuite appliqués aux équations d'onde avec contrôle au bord et contrôle distribué.
Mathematics Subject Classification: 93B05 / 42C15
Key words: Controllability / exponential families.
© EDP Sciences, SMAI, 1999
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