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Control Norms for Large Control Times

Published online by Cambridge University Press:  15 August 2002

Sergei Ivanov
Sergei Ivanov*
Affiliation:
Russian Center of Laser Physics, St. Petersburg University, Ul'yanovskaya ul. 1, Petrodvorets, St. Petersburg 198904, Russia; Sergei.Ivanov@pobox.spbu.ru.
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Abstract

A control system of the second order in time with control $u=u(t) \in L^2([0,T];U)$ 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 $1/\sqrt T$ while the $L^1([0,T];U)$–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.

Keywords

Controllabilityexponential families.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 4 , 1999 , pp. 405 - 418
Copyright
© EDP Sciences, SMAI, 1999

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