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

• Autorzy: Yuncheng You
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Ginzburg-Landau equation; optimal control; differential inclusion; superconductivity

Kategorie tematyczne

• 82D55: Superconductors
• 35Q55: NLS-like equations (nonlinear Schr\"odinger)
• 49N35: Optimal feedback synthesis
• 35B27: Homogenization; equations in media with periodic structure
• 49J20: Optimal control problems involving partial differential equations
• 35K55: Nonlinear parabolic equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 1996
• Tom: 16
• Numer: 1
• Strony: 5-41

Daty

wydano

1996

Twórcy

autor

Yuncheng You

• Department of Mathematics, University of South Florida, Tampa, FL 33620-5700, USA

Bibliografia

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