On the Explicit Scheme with Variable Time Steps for Solving the Parabolic Optimal Control Problem

On the Explicit Scheme with Variable Time Steps for Solving the Parabolic Optimal Control Problem

The paper deals with the optimal control problem, including the linear parabolic equation as a state problem. Pointwise constraints are imposed on the control function. The objective functional involves the observation function in the entire space-time domain. The optimal control problem is approxim...

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Bibliographic Details
Main Author: A.D. Romanenko
Format: Article
Language:Russian
Published: Kazan Federal University 2016-09-01
Series:Učënye Zapiski Kazanskogo Universiteta: Seriâ Fiziko-Matematičeskie Nauki
Subjects:
optimal control
constraint on control
variable step
iterative method
Online Access:http://kpfu.ru/portal/docs/F687914633/158_3_phys_mat_5.pdf
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spelling doaj-b6c7720db7c14937989e983dcd6c28172020-11-24T22:29:17ZrusKazan Federal UniversityUčënye Zapiski Kazanskogo Universiteta: Seriâ Fiziko-Matematičeskie Nauki2541-77462500-21982016-09-011583376387On the Explicit Scheme with Variable Time Steps for Solving the Parabolic Optimal Control ProblemA.D. Romanenko0Kazan Federal University, Kazan, 420008 RussiaThe paper deals with the optimal control problem, including the linear parabolic equation as a state problem. Pointwise constraints are imposed on the control function. The objective functional involves the observation function in the entire space-time domain. The optimal control problem is approximated by a finite dimensional problem with mesh approximation of the state equation by the explicit (forward Euler) mesh scheme with variable time steps. The existence of unique solutions for the continuous and mesh optimal control problems is proved. The Uzawa-type iterative method is used for solving the finite dimensional optimal control problem. The results of numerical experiments are presented.http://kpfu.ru/portal/docs/F687914633/158_3_phys_mat_5.pdfoptimal controlconstraint on controlvariable stepiterative method
collection DOAJ
language Russian
format Article
sources DOAJ
author A.D. Romanenko
spellingShingle A.D. Romanenko
On the Explicit Scheme with Variable Time Steps for Solving the Parabolic Optimal Control Problem
Učënye Zapiski Kazanskogo Universiteta: Seriâ Fiziko-Matematičeskie Nauki
optimal control
constraint on control
variable step
iterative method
author_facet A.D. Romanenko
author_sort A.D. Romanenko
title On the Explicit Scheme with Variable Time Steps for Solving the Parabolic Optimal Control Problem
title_short On the Explicit Scheme with Variable Time Steps for Solving the Parabolic Optimal Control Problem
title_full On the Explicit Scheme with Variable Time Steps for Solving the Parabolic Optimal Control Problem
title_fullStr On the Explicit Scheme with Variable Time Steps for Solving the Parabolic Optimal Control Problem
title_full_unstemmed On the Explicit Scheme with Variable Time Steps for Solving the Parabolic Optimal Control Problem
title_sort on the explicit scheme with variable time steps for solving the parabolic optimal control problem
publisher Kazan Federal University
series Učënye Zapiski Kazanskogo Universiteta: Seriâ Fiziko-Matematičeskie Nauki
issn 2541-7746
2500-2198
publishDate 2016-09-01
description The paper deals with the optimal control problem, including the linear parabolic equation as a state problem. Pointwise constraints are imposed on the control function. The objective functional involves the observation function in the entire space-time domain. The optimal control problem is approximated by a finite dimensional problem with mesh approximation of the state equation by the explicit (forward Euler) mesh scheme with variable time steps. The existence of unique solutions for the continuous and mesh optimal control problems is proved. The Uzawa-type iterative method is used for solving the finite dimensional optimal control problem. The results of numerical experiments are presented.
topic optimal control
constraint on control
variable step
iterative method
url http://kpfu.ru/portal/docs/F687914633/158_3_phys_mat_5.pdf
work_keys_str_mv AT adromanenko ontheexplicitschemewithvariabletimestepsforsolvingtheparabolicoptimalcontrolproblem
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