scholarly journals On the existence and uniqueness of the solution of an optimal control problem for Schrödinger equation

2019 ◽  
Vol 12 (3) ◽  
pp. 503-512
Author(s):  
Gökçe Dİlek Küçük ◽  
◽  
Gabil Yagub ◽  
Ercan Çelİk ◽  
◽  
...  
Keyword(s):  
Optimal Control ◽  
Schrödinger Equation ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Uniqueness Of The Solution

scholarly journals A Note on Optimal Control Problem Governed by Schrödinger Equation

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Yusuf Koçak ◽  
Ercan Çelik ◽  
Nigar Yıldırım Aksoy
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Schrödinger Equation ◽  
Optimal Control Problem ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Optimal Solution ◽  
Necessary Condition ◽  
Existence And Uniqueness Theorem ◽  
The Cost

AbstractIn 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.

scholarly journals An optimal control problem with final observation for systems governed by nonlinear Schrödinger equation

Filomat ◽  
2016 ◽  
Vol 30 (3) ◽  
pp. 649-665 ◽  
Author(s):  
Aksoy Yildirim ◽  
Eray Aksoy ◽  
Yusuf Kocak
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence And Uniqueness ◽  
Necessary Optimality Condition ◽  
Uniqueness Of The Solution ◽  
Variational Form ◽  
Final Observation ◽  
The First Variation ◽  
Objective Functional

In this paper, an optimal control problem with final observation for systems governed by nonlinear time-dependent Schr?dinger equation is studied. The existence and uniqueness of the solution of considered optimal control problem are proved. The first variation of objective functional is obtained and a necessary optimality condition in the variational form is given.

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