Optimal Control with Time Delays via the Penalty Method

Optimal Control with Time Delays via the Penalty Method

We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main resul...

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Main Authors: Mohammed Benharrat, Delfim F. M. Torres
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2014/250419
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spelling doaj-3bdd5ba3af2d46098f2805b26a14a3ef2020-11-25T01:35:50ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472014-01-01201410.1155/2014/250419250419Optimal Control with Time Delays via the Penalty MethodMohammed Benharrat0Delfim F. M. Torres1Département de Mathématiques et Informatique, Ecole National Polytechnique d’Oran (Ex. ENSET d’Oran), 1523 El M’Naouar, Oran, AlgeriaDepartment of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193 Aveiro, PortugalWe prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main result gives a convergence theorem, allowing us to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations.http://dx.doi.org/10.1155/2014/250419
collection DOAJ
language English
format Article
sources DOAJ
author Mohammed Benharrat
Delfim F. M. Torres
spellingShingle Mohammed Benharrat
Delfim F. M. Torres
Optimal Control with Time Delays via the Penalty Method
Mathematical Problems in Engineering
author_facet Mohammed Benharrat
Delfim F. M. Torres
author_sort Mohammed Benharrat
title Optimal Control with Time Delays via the Penalty Method
title_short Optimal Control with Time Delays via the Penalty Method
title_full Optimal Control with Time Delays via the Penalty Method
title_fullStr Optimal Control with Time Delays via the Penalty Method
title_full_unstemmed Optimal Control with Time Delays via the Penalty Method
title_sort optimal control with time delays via the penalty method
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2014-01-01
description We prove necessary optimality conditions of Euler-Lagrange type for a problem of the calculus of variations with time delays, where the delay in the unknown function is different from the delay in its derivative. Then, a more general optimal control problem with time delays is considered. Main result gives a convergence theorem, allowing us to obtain a solution to the delayed optimal control problem by considering a sequence of delayed problems of the calculus of variations.
url http://dx.doi.org/10.1155/2014/250419
work_keys_str_mv AT mohammedbenharrat optimalcontrolwithtimedelaysviathepenaltymethod
AT delfimfmtorres optimalcontrolwithtimedelaysviathepenaltymethod
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