A Singular Perturbation Problem in Exact Controllability of the Maxwell System

John E. Lagnese

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

  • Volume: 6, page 275-289
  • ISSN: 1292-8119

Abstract

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This paper studies the exact controllability of the Maxwell system in a bounded domain, controlled by a current flowing tangentially in the boundary of the region, as well as the exact controllability the same problem but perturbed by a dissipative term multiplied by a small parameter in the boundary condition. This boundary perturbation improves the regularity of the problem and is therefore a singular perturbation of the original problem. The purpose of the paper is to examine the connection, for small values of the perturbation parameter, between observability estimates for the two systems, and between the optimality systems corresponding to the problem of norm minimum exact control of the solutions of the two systems from the rest state to a specified terminal state.

How to cite

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Lagnese, John E.. "A Singular Perturbation Problem in Exact Controllability of the Maxwell System." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 275-289. <http://eudml.org/doc/197366>.

@article{Lagnese2010,
abstract = { This paper studies the exact controllability of the Maxwell system in a bounded domain, controlled by a current flowing tangentially in the boundary of the region, as well as the exact controllability the same problem but perturbed by a dissipative term multiplied by a small parameter in the boundary condition. This boundary perturbation improves the regularity of the problem and is therefore a singular perturbation of the original problem. The purpose of the paper is to examine the connection, for small values of the perturbation parameter, between observability estimates for the two systems, and between the optimality systems corresponding to the problem of norm minimum exact control of the solutions of the two systems from the rest state to a specified terminal state. },
author = {Lagnese, John E.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Maxwell system; exact controllability; singular perturbation.; singular perturbation; robustness; minimum norm control},
language = {eng},
month = {3},
pages = {275-289},
publisher = {EDP Sciences},
title = {A Singular Perturbation Problem in Exact Controllability of the Maxwell System},
url = {http://eudml.org/doc/197366},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Lagnese, John E.
TI - A Singular Perturbation Problem in Exact Controllability of the Maxwell System
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 6
SP - 275
EP - 289
AB - This paper studies the exact controllability of the Maxwell system in a bounded domain, controlled by a current flowing tangentially in the boundary of the region, as well as the exact controllability the same problem but perturbed by a dissipative term multiplied by a small parameter in the boundary condition. This boundary perturbation improves the regularity of the problem and is therefore a singular perturbation of the original problem. The purpose of the paper is to examine the connection, for small values of the perturbation parameter, between observability estimates for the two systems, and between the optimality systems corresponding to the problem of norm minimum exact control of the solutions of the two systems from the rest state to a specified terminal state.
LA - eng
KW - Maxwell system; exact controllability; singular perturbation.; singular perturbation; robustness; minimum norm control
UR - http://eudml.org/doc/197366
ER -

References

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