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...

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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
Description
Summary: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.
ISSN:2391-5471

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