The solvability of the optimal control problem for a nonlinear Schrödinger equation

Authors

DOI:

https://doi.org/10.11121/ijocta.2023.1371

Keywords:

Optimal control problem, Schrödinger equation, Frechet differentiability, Optimality conditions

Abstract

In this paper, we analyze the solvability of the optimal control problem for a nonlinear Schr\"{o}dinger equation. A Lions-type functional is considered as the objective functional. First, it is shown that the optimal control problem has at least one solution. Later, the Frechet differentiability of the objective functional is proved and a formula is obtained for its gradient. Finally, a necessary optimality condition is derived.

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Author Biographies

Nigar Yildirim Aksoy, Department of Mathematics, Faculty of Arts and Sciences, Kafkas University, Kars, Turkey

Nigar Yildirim Aksoy received her Ph.D. degree from the Department of Mathematics, Atatürk University in 2009. She is an Associate Professor in the Department of Mathematics, at Kafkas University. Her research interests include optimal control theory, variational Methods, and numerical methods.

Ercan Çelik, Department of Applied Mathematics and Informatics, Kyrgyz-Turkish Manas University, Bishkek, Kyrgyzstan

Ercan Celik received his Ph.D. degree from the Department of Mathematics, Atatürk University in 2002. He is a Professor in the Department of Applied Mathematics and Informatics, Kyrgyz-Turkish Manas University. His research interests include applied mathematics, numerical analysis, fractional calculus, optimal control, and differential algebraic equations.

Muhammed Emin Dadas, Department of Mathematics, Faculty of Arts and Sciences, Kafkas University, Kars, Turkey

Muhammed Emin Dadas received his M.Sc. degree from the Department of Mathematics, Kafkas University in 2019. His research interests include optimal control theory and numerical methods.

 

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Published

2023-07-29
CITATION
DOI: 10.11121/ijocta.2023.1371
Published: 2023-07-29

How to Cite

Yildirim Aksoy, N., Çelik, E., & Dadas, M. E. (2023). The solvability of the optimal control problem for a nonlinear Schrödinger equation. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 13(2), 269–276. https://doi.org/10.11121/ijocta.2023.1371

Issue

Vol. 13 No. 2 (2023): IJOCTA

Section

Research Articles

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Copyright (c) 2023 Nigar Yildirim Aksoy, Ercan Çelik, Muhammed Emin Dadas

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