scholarly journals Optimal Control of PDEs in a Complex Space Setting: Application to the Schrödinger Equation

2019 ◽  
Vol 57 (2) ◽  
pp. 1390-1412
Author(s):  
M. Soledad Aronna ◽  
Joseph Frédéric Bonnans ◽  
Axel Kröner
Keyword(s):  
Optimal Control ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Complex Space ◽  
Space Setting ◽  
Control Of Pdes

scholarly journals Quantum Optimal Control for Bose-Einstein-Condensates at Complex Space

2021 ◽  
Author(s):  
Quan-Fang Wang
Keyword(s):  
Optimal Control ◽  
Hilbert Spaces ◽  
Schrodinger Equation ◽  
Quantum Control ◽  
Complex Space ◽  
Pitaevskii Equation ◽  
Interesting Topic ◽  
Quantum Optimal Control ◽  
Control Target ◽  
Bose Einstein

Quantum control of Bose-Einstein-Condensates is interesting topic in the areas of control and physics. In this work, Gross-Pitaevskii equation expressed Bose-Einstein-Condensates is considered as control target. Full theoretical proof for the existence of quantum optimal control is provided for cubical Schrodinger equation in complex Hilbert spaces.

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 Optimal control of bilinear systems in a complex space setting

2017 ◽  
Vol 50 (1) ◽  
pp. 2872-2877 ◽  
Author(s):  
M.S. Aronna ◽  
J.F. Bonnans ◽  
A. Kröner
Keyword(s):  
Optimal Control ◽  
Complex Space ◽  
Bilinear Systems ◽  
Space Setting
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