A Note on Optimal Control Problem Governed by Schrödinger Equation

A Note on Optimal Control Problem Governed by Schrödinger Equation

In this work, we present some results showing the controllability of the linear Schrödinger equation with complex potentials. Firstly we investigate the existence and uniqueness theorem for solution of the considered problem. Then we find the gradient of the cost functional with the help of Hamilton...

Full description

Bibliographic Details
Main Authors: Koçak Yusuf, Çelik Ercan, Aksoy Nigar Yıldırım
Format: Article
Language:English
Published: De Gruyter 2015-12-01
Series:Open Physics
Subjects:
Schrödinger equation
Optimal Control
Hamilton-Pontryagin functions
Fréchet derivative
Online Access:http://www.degruyter.com/view/j/phys.2015.13.issue-1/phys-2015-0051/phys-2015-0051.xml?format=INT
id doaj-3143d24bdc2244f89b7d8a23cf822730
record_format Article
spelling doaj-3143d24bdc2244f89b7d8a23cf8227302020-11-24T21:40:09ZengDe GruyterOpen Physics2391-54712015-12-0113110.1515/phys-2015-0051phys-2015-0051A Note on Optimal Control Problem Governed by Schrödinger EquationKoçak Yusuf0Çelik Ercan1Aksoy Nigar Yıldırım2Department of Mathematics, Ağrı İbrahim Çeçen Universty,Faculty of Science and Art,Ağrı,TurkeyDepartment of Mathematics, Ataturk University, Faculty of Science, Erzurum, TurkeyDepartment of Mathematics, Kafkas University, Faculty of Science and Art, Kars, TurkeyIn this work, we present some results showing the controllability of the linear Schrödinger equation with complex potentials. Firstly we investigate the existence and uniqueness theorem for solution of the considered problem. Then we find the gradient of the cost functional with the help of Hamilton-Pontryagin functions. Finally we state a necessary condition in the form of variational inequality for the optimal solution using this gradient.http://www.degruyter.com/view/j/phys.2015.13.issue-1/phys-2015-0051/phys-2015-0051.xml?format=INTSchrödinger equationOptimal Control Hamilton-Pontryagin functionsFréchet derivative
collection DOAJ
language English
format Article
sources DOAJ
author Koçak Yusuf
Çelik Ercan
Aksoy Nigar Yıldırım
spellingShingle Koçak Yusuf
Çelik Ercan
Aksoy Nigar Yıldırım
A Note on Optimal Control Problem Governed by Schrödinger Equation
Open Physics
Schrödinger equation
Optimal Control
Hamilton-Pontryagin functions
Fréchet derivative
author_facet Koçak Yusuf
Çelik Ercan
Aksoy Nigar Yıldırım
author_sort Koçak Yusuf
title A Note on Optimal Control Problem Governed by Schrödinger Equation
title_short A Note on Optimal Control Problem Governed by Schrödinger Equation
title_full A Note on Optimal Control Problem Governed by Schrödinger Equation
title_fullStr A Note on Optimal Control Problem Governed by Schrödinger Equation
title_full_unstemmed A Note on Optimal Control Problem Governed by Schrödinger Equation
title_sort note on optimal control problem governed by schrödinger equation
publisher De Gruyter
series Open Physics
issn 2391-5471
publishDate 2015-12-01
description In this work, we present some results showing the controllability of the linear Schrödinger equation with complex potentials. Firstly we investigate the existence and uniqueness theorem for solution of the considered problem. Then we find the gradient of the cost functional with the help of Hamilton-Pontryagin functions. Finally we state a necessary condition in the form of variational inequality for the optimal solution using this gradient.
topic Schrödinger equation
Optimal Control
Hamilton-Pontryagin functions
Fréchet derivative
url http://www.degruyter.com/view/j/phys.2015.13.issue-1/phys-2015-0051/phys-2015-0051.xml?format=INT
work_keys_str_mv AT kocakyusuf anoteonoptimalcontrolproblemgovernedbyschrodingerequation
AT celikercan anoteonoptimalcontrolproblemgovernedbyschrodingerequation
AT aksoynigaryıldırım anoteonoptimalcontrolproblemgovernedbyschrodingerequation
AT kocakyusuf noteonoptimalcontrolproblemgovernedbyschrodingerequation
AT celikercan noteonoptimalcontrolproblemgovernedbyschrodingerequation
AT aksoynigaryıldırım noteonoptimalcontrolproblemgovernedbyschrodingerequation
_version_ 1725927914513367040

Similar Items