About: First order conditions for generalized variational problems over time scales

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper we derive the weak Pontryagin principle for generalized optimal control problems over time scales. Three types of problems are considered, namely (i) the problems involving the values of the state endpoints in the Lagrangian and the dynamics, (ii) the problems with an integral of the state in the Lagrangian and the dynamics, and (iii) the isoperimetric problems. As special cases we obtain the first order optimality conditions for the corresponding calculus of variations problems, which have been of a recent interest in the literature. Our method is based on transforming the generalized optimal control or calculus of variations problem into a traditional optimal control problem on time scales, to which the known weak Pontryagin principle can be applied. In this paper we derive the weak Pontryagin principle for generalized optimal control problems over time scales. Three types of problems are considered, namely (i) the problems involving the values of the state endpoints in the Lagrangian and the dynamics, (ii) the problems with an integral of the state in the Lagrangian and the dynamics, and (iii) the isoperimetric problems. As special cases we obtain the first order optimality conditions for the corresponding calculus of variations problems, which have been of a recent interest in the literature. Our method is based on transforming the generalized optimal control or calculus of variations problem into a traditional optimal control problem on time scales, to which the known weak Pontryagin principle can be applied. (en)
Title	First order conditions for generalized variational problems over time scales First order conditions for generalized variational problems over time scales (en)
skos:prefLabel	First order conditions for generalized variational problems over time scales First order conditions for generalized variational problems over time scales (en)
skos:notation	RIV/00216224:14310/11:00049947!RIV12-GA0-14310___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GAP201/10/1032), P(ME 891), Z(MSM0021622409)
http://linked.open...iv/cisloPeriodika	9
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Šimon Hilscher, Roman
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	199836
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/11:00049947
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Time scale; Optimal control problem; Weak Pontryagin principle; First order optimality conditions; Weak local minimum; Calculus of variations problem; Euler-Lagrange equation; Transversality condition; Natural boundary condition; Isoperimetric problem (en)
http://linked.open.../riv/klicoveSlovo	Calculus of variations problem Euler-Lagrange equation First order optimality conditions Isoperimetric problem Natural boundary condition Optimal control problem Transversality condition Weak Pontryagin principle Weak local minimum Time scale
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[20C4C7292A68]
http://linked.open...i/riv/nazevZdroje	Computers & Mathematics with Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Difference equations and dynamic equations on time scales III http://linked.opendata.cz/resource/domain/vavai/projekt/ME%20891
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	62
http://linked.open...iv/tvurceVysledku	Zeidan, Vera Michel Šimon Hilscher, Roman
http://linked.open...ain/vavai/riv/wos	000296987000020
http://linked.open...n/vavai/riv/zamer	Matematické struktury a jejich fyzikální aplikace
issn	0898-1221
number of pages	14 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.camwa.2011.08.065
http://localhost/t...ganizacniJednotka	14310

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