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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.