On optimal control of a charged particle in a varying electromagnetic field

Aksoy, Nigar Yildirim; Çelık, Ercan; Zengin, M.

doi:10.1080/17455030.2022.2142695

Cited by 2 publications

(5 citation statements)

References 10 publications

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“…is an enhancement given to any q ∈ Q ad such that q + δq ∈ Q ad , and the function δu is a solution of the following problem [15]:…”

Section: Theoremmentioning

confidence: 99%

“…Also, based on the results in [15], we write the following theorems for the existence of an optimal solution: Theorem 2. If the conditions of Theorem 1 are satisfied, then there exists a unique solution of the OCP on a dense subset W 0 ⊂ W for any ω ∈ W 0 and α > 0 .…”

Section: Introductionmentioning

confidence: 99%

“…It should be noted here that the OCPs with a boundary functional for the LSEwSGT have been hardly analyzed. In [15,28], the authors demonstrate the existence of optimal solutions for OCPs with a boundary functional for the LSEwSGT.…”

Section: Introductionmentioning

confidence: 99%

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A Necessary Optimality Condition on the Control of a Charged Particle

Aksoy,

Celik,

Zengin

2024

Symmetry

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We consider an optimal control problem with the boundary functional for a Schrödinger equation describing the motion of a charged particle. By using the existence of an optimal solution, we search the necessary optimality conditions for the examined control problem. First, we constitute an adjoint problem by a Lagrange multiplier that is related to constraints of theory on symmetries and conservation laws. The adjoint problem obtained is a boundary value problem with a nonhomogeneous boundary condition. We prove the existence and uniqueness of the solution of the adjoint problem. Then, we demonstrate the differentiability of the objective functional in the sense of Frechet and get a formula for its gradient. Finally, we give a necessary optimality condition in the form of a variational inequality.

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“…is an enhancement given to any q ∈ Q ad such that q + δq ∈ Q ad , and the function δu is a solution of the following problem [15]:…”

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Necessary Optimality Condition on the Control of a Charged Particle

Aksoy,

Celik,

Zengin

2024

Symmetry

Self Cite

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“…Assume that the conditions of Theorem 4 are satisfied. Then, J α (p) is a differentiable functional on P and moreover, its gradient is given by formula (29).…”

Section: The Gradient Of Functional and A Necessary Optimality Conditionmentioning

confidence: 99%

“…In [23][24][25][26][27], the OCPs with Lions functional has been studied and the controlled system is stated by linear or nonlinear Schrödinger equations. Also, in [28][29][30], the OCPs for systems whose state is expressed by the Schrödinger equation with the boundary functional has been studied.…”

Section: Introductionmentioning

confidence: 99%

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

Yildirim Aksoy,

Çelik,

Dadas

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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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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On optimal control of a charged particle in a varying electromagnetic field

Cited by 2 publications

References 10 publications

A Necessary Optimality Condition on the Control of a Charged Particle

A Necessary Optimality Condition on the Control of a Charged Particle

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

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