Control Norms for Large Control Times

Sergei Ivanov

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 4, page 405-418
  • ISSN: 1292-8119

Abstract

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A control system of the second order in time with control u = u ( t ) ∈ 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 / 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.

How to cite

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Ivanov, Sergei. "Control Norms for Large Control Times." ESAIM: Control, Optimisation and Calculus of Variations 4 (2010): 405-418. <http://eudml.org/doc/197305>.

@article{Ivanov2010,
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. },
author = {Ivanov, Sergei},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Controllability; exponential families.; families of exponentials; biorthogonal functions; Riesz bases},
language = {eng},
month = {3},
pages = {405-418},
publisher = {EDP Sciences},
title = {Control Norms for Large Control Times},
url = {http://eudml.org/doc/197305},
volume = {4},
year = {2010},
}

TY - JOUR
AU - Ivanov, Sergei
TI - Control Norms for Large Control Times
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 4
SP - 405
EP - 418
AB - 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.
LA - eng
KW - Controllability; exponential families.; families of exponentials; biorthogonal functions; Riesz bases
UR - http://eudml.org/doc/197305
ER -

References

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