Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


Preferences help
enabled [disable] Abstract
Number of results

Journal

2015 | 13 | 1 |

Article title

A Note on Optimal Control Problem Governed by
Schrödinger Equation

Content

Title variants

Languages of publication

EN

Abstracts

EN
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.

Publisher

Journal

Year

Volume

13

Issue

1

Physical description

Dates

accepted
26 - 11 - 2015
received
28 - 9 - 2015
online
31 - 12 - 2015

Contributors

author
  • Department of Mathematics,
    Ağrı İbrahim Çeçen Universty,Faculty of Science and
    Art,Ağrı,Turkey
author
  • Department of Mathematics, Ataturk University,
    Faculty of Science, Erzurum, Turkey
  • Department of Mathematics, Kafkas University,
    Faculty of Science and Art, Kars, Turkey

References

  • [1] A. D. Iskenderov, G. Ya. Yagubov, A variational method for solvingthe inverse problem of determining the quantum- mechanicalpotential, Soviet Math. Dokl.(English Trans.). AMS 38(1989)
  • [2] A. D. Iskenderov, G. Ya. Yagubov, Optimal control of nonlinearquantum-mechanical systems, Automatica and Telemechanic12(1989) 27-38
  • [3] A. D. Iskenderov, Definition of a potential in Schrödingers’ nonstationaryequation. In: Problemi moton. Modelşrovania andopmolno go upravleva, Bakü, 2001, pp.6-36 (in Russian)
  • [4] M. Goebel, On existence of optimal control, Math. Nachr. 1979.Vol.93, pp.67-73
  • [5] J. L. Lions, Optimal Control of Systems Governed by Partial DifferentialEquations, Springer, Berlin, 1971
  • [6] E. Zuazua, Remarks on the controllability of the Schrödingerequation, Quantum control: mathematical and numerical challenges,2003, Vol.33, pp. 193-211
  • [7] E. Zuazua, An introduction to the controllability of partial differentialequations, Quelques questions de théorie du contrôle,2004,
  • [8] E. Zuazua, Controllability of partial differential equations andits semi-discrete approximations, Discrete and continuous dynamicalsystems, 2004, 8 (2), 469-517
  • [9] N.Y. Aksoy, B. Yildiz, H. Yetiskin, Variational problem with complexcoeflcient of a nonlinear Schrödinger equation Proceedingsof the Indian Academy of Sciences:Mathematical Sciences,2012, 122 (3), pp. 469-484
  • [10] Y. Koçak, E. Çelik, Optimal control problem for stationary quasiopticequations, Boundary Value Problems 2012, 2012:151
  • [11] Y. Koçak, M.A. Dokuyucu, E. Çelik, Well-Posedness of OptimalControl Problem for the Schrödinger Equations with ComplexPotential, International Journal of Mathematics and Computation,2015, 26 (4), 11-16
  • [12] G.Ya. Yagubov, N.S. Ibrahimov, Optimal control problem fornonstationary quasi optic equation, Problems of mathematicalmodeling and optimal control, Baku, 2001, pp. 49-57 (in Russian).
  • [13] H. yetişkin., M. Subaşı., On the optimal control problem forSchrödinger equation with complex potential, Applied Mathematicsand Computation, 2010, 216(7), pp. 1896–1902
  • [14] G.Ya. Yagubov, M.A. Musayeva, On the identification problemfor nonlinear Schrödinger equation, Differentsial’niye uravneniya3(12) (1997) 1691–1698 (in Russian)
  • [15] M. Koksal, M.E. Koksal, Commutativity of Linear Time-varyingDifferential Systems with Non-zero Initial Conditions: A Reviewand Some New Extensions,Mathematical Problems in Engineering,2011 (2011) Article Number: 678575, 1-25, 2
  • [16] M. Koksal, M.E. Koksal, Commutativity of Cascade ConnectedDiscrete Time Linear Time-Varying Systems, Transactions of theInstitute of Measurement and Control, 2015, 37 (5) 615-622
  • [17] M.A. Vorontsov, V. I. Shmalgauzen, Principles of adaptive optics.Moscow, Izdatel’stvo Nauka, 1985, 336 p. (in Russian)
  • [18] K. Yosida, Functional analysis. Springer, 1980
  • [19] O.A. Ladyzhanskaya, V.A. Sollonnikov, N.M. Uraltseva, Linearand Quasi- Linear Equations of Parabolic Type, Translation ofMathematical Monographs. AMS, Rhode Island, 1968
  • [20] N.S. Ibrahimov, Solubility of initial-boundary value problemsfor linear stationary equation of quasi optic. Journal of QafqazUniversity. 2010, No:29, pp. 61-70 (in Russian)

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_1515_phys-2015-0051
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.