Optimal feedback control of Ginzburg-Landau equation for superconductivity via differential inclusion

Yuncheng You

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (1996)

  • Volume: 16, Issue: 1, page 5-41
  • ISSN: 1509-9407

Abstract

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Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear coefficient control problem in Hilbert spaces. The global existence and regularity of solutions of the state equation, the existence of optimal control, and the maximum principle as a necessary condition satisfied by optimal control are proved. By proving the local Lipschitz continuity of the value functions and by using lower Dini derivatives, an optimal synthesis (i.e. optimal feedback control) is obtained via solving a differential inclusion.

How to cite

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Yuncheng You. "Optimal feedback control of Ginzburg-Landau equation for superconductivity via differential inclusion." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 16.1 (1996): 5-41. <http://eudml.org/doc/275907>.

@article{YunchengYou1996,
abstract = {Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear coefficient control problem in Hilbert spaces. The global existence and regularity of solutions of the state equation, the existence of optimal control, and the maximum principle as a necessary condition satisfied by optimal control are proved. By proving the local Lipschitz continuity of the value functions and by using lower Dini derivatives, an optimal synthesis (i.e. optimal feedback control) is obtained via solving a differential inclusion.},
author = {Yuncheng You},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {Ginzburg-Landau equation; optimal control; differential inclusion; superconductivity; superconductors; regularity of solutions; maximum principle; necessary condition},
language = {eng},
number = {1},
pages = {5-41},
title = {Optimal feedback control of Ginzburg-Landau equation for superconductivity via differential inclusion},
url = {http://eudml.org/doc/275907},
volume = {16},
year = {1996},
}

TY - JOUR
AU - Yuncheng You
TI - Optimal feedback control of Ginzburg-Landau equation for superconductivity via differential inclusion
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 1996
VL - 16
IS - 1
SP - 5
EP - 41
AB - Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear coefficient control problem in Hilbert spaces. The global existence and regularity of solutions of the state equation, the existence of optimal control, and the maximum principle as a necessary condition satisfied by optimal control are proved. By proving the local Lipschitz continuity of the value functions and by using lower Dini derivatives, an optimal synthesis (i.e. optimal feedback control) is obtained via solving a differential inclusion.
LA - eng
KW - Ginzburg-Landau equation; optimal control; differential inclusion; superconductivity; superconductors; regularity of solutions; maximum principle; necessary condition
UR - http://eudml.org/doc/275907
ER -

References

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