Optimal control problem for nonstationary Schrödinger equation

Yıldız, Bünyamin; Kilicoglu, Oguz; Yagubov, Gabil

doi:10.1002/num.20395

Cited by 7 publications

(6 citation statements)

References 2 publications

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“…More recently, optimal control problems for linear Schrödinger equations have been studied in [2,4,15]. In addition, numerical questions related to quantum control are studied in [3,30]. Among these papers, the work in [15] appears closest to our effort.…”

Section: 3mentioning

confidence: 99%

Optimal Bilinear Control of Gross--Pitaevskii Equations

Hintermüller¹,

Marahrens²,

Markowich³

et al. 2013

SIAM J. Control Optim.

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Abstract.A mathematical framework for optimal bilinear control of nonlinear Schrödinger equations of Gross-Pitaevskii type arising in the description of Bose-Einstein condensates is presented. The obtained results generalize earlier efforts found in the literature in several aspects. In particular, the cost induced by the physical workload over the control process is taken into account rather than the often used L 2 -or H 1 -norms for the cost of the control action. Well-posedness of the problem and existence of an optimal control are proved. In addition, the first order optimality system is rigorously derived. Also a numerical solution method is proposed, which is based on a Newton-type iteration, and used to solve several coherent quantum control problems.

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Section: 3mentioning

confidence: 99%

Optimal Bilinear Control of Gross--Pitaevskii Equations

Hintermüller¹,

Marahrens²,

Markowich³

et al. 2013

SIAM J. Control Optim.

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“…Many problems in financial derivatives [1], option pricing [2], chemical diffusion [3], computational fluid dynamics [4], hydrodynamics [5], and control theory [6] can be modeled using partial differential equations (PDEs). In recent years, a lot of attention has been devoted to the study of nonlinear PDEs and methods for numerical solutions of nonlinear problems.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Alternating Direction Explicit Method for Solving a Nonlinear Partial Differential Equation

Pourghanbar

Manafian

Ranjbar

et al. 2020

Mathematical Problems in Engineering

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In this paper, the Saul’yev finite difference scheme for a fully nonlinear partial differential equation with initial and boundary conditions is analyzed. The main advantage of this scheme is that it is unconditionally stable and explicit. Consistency and monotonicity of the scheme are discussed. Several finite difference schemes are used to compare the Saul’yev scheme with them. Numerical illustrations are given to demonstrate the efficiency and robustness of the scheme. In each case, it is found that the elapsed time for the Saul’yev scheme is shortest, and the solution by the Saul’yev scheme is nearest to the Crank–Nicolson method.

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“…The optimal control problem (OCP) is to obtain a control function that minimizes or maximizes known performance index governing by the system state equations together with the constraints. Their applications appear in many disciplines, economics, management, and engineering [1][2][3].…”

Section: -Introductionmentioning

confidence: 99%

State Parameterization Basic Spline Functions for Trajectory Optimization

Delphi¹

2019

Journal of Natural Sciences, Life and Applied Sciences

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An important type of basic functions named basis spline (B-spline) is provided a simpler approximate and more stable approach to solve problems in optimal control. Furthermore, it can be proved that with special knot sequence, the B-spline basis are exactly Bernstein polynomials. The approximate technique is based on state variable is approximate as a linear combination of B-spline then anon linear optimization problem is obtained and the optimal coefficients are calculated using an iterative algorithm. Two different examples are tested using the proposed algorithm.

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Optimal control problem for nonstationary Schrödinger equation

Cited by 7 publications

References 2 publications

Optimal Bilinear Control of Gross--Pitaevskii Equations

Optimal Bilinear Control of Gross--Pitaevskii Equations

An Efficient Alternating Direction Explicit Method for Solving a Nonlinear Partial Differential Equation

State Parameterization Basic Spline Functions for Trajectory Optimization

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