Podmínky Legendreova, Jacobiho a Riccatiho typu pro variační problém na time scales s aplikací

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F07%3A00019435" target="_blank" >RIV/00216224:14310/07:00019435 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application

Popis výsledku v původním jazyce

A time scale quadratic problem J with piecewise right-dense continuous coefficients and one varying endpoint is considered. Such problems are ``hybrid'', since they include mixing of continuous- and discrete-time problems. A new notion of a generalized conjugate point involving ``dynamic'' (hybrid) systems and comprising as special cases those known for the continuous- and discrete-time settings is introduced. A type of a strengthened Legendre condition is identified and used to establish characterizations of the nonnegativity and positivity of J in terms of (i) the nonexistence of such conjugate points, (ii) the natural conjoined basis of the associated time scale Jacobi equation, and (iii) a solution of the corresponding time scale Riccati equation.These results furnish second order necessary optimality conditions for a nonlinear time scale variational problem. Furthermore, we present an example of an optimal impulsive control problem and we show how this problem can be reduced to a

Název v anglickém jazyce

Legendre, Jacobi, and Riccati type conditions for time scale variational problem with application

Popis výsledku anglicky

A time scale quadratic problem J with piecewise right-dense continuous coefficients and one varying endpoint is considered. Such problems are ``hybrid'', since they include mixing of continuous- and discrete-time problems. A new notion of a generalized conjugate point involving ``dynamic'' (hybrid) systems and comprising as special cases those known for the continuous- and discrete-time settings is introduced. A type of a strengthened Legendre condition is identified and used to establish characterizations of the nonnegativity and positivity of J in terms of (i) the nonexistence of such conjugate points, (ii) the natural conjoined basis of the associated time scale Jacobi equation, and (iii) a solution of the corresponding time scale Riccati equation.These results furnish second order necessary optimality conditions for a nonlinear time scale variational problem. Furthermore, we present an example of an optimal impulsive control problem and we show how this problem can be reduced to a

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2007

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Dynamic Systems and Applications

ISSN

1056-2176

e-ISSN

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Svazek periodika

16

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

30

Strana od-do

451-480

Kód UT WoS článku

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EID výsledku v databázi Scopus

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