Symplectic structure of Jacobi systems on time scales

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F10%3A00040560" target="_blank" >RIV/00216224:14310/10:00040560 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Symplectic structure of Jacobi systems on time scales

Original language description

In this paper we study the structure of the Jacobi system for optimal control problems on time scales. Under natural and minimal invertibility assumptions on the coefficients we prove that the Jacobi system is a time scale symplectic system and not necessarily a Hamiltonian system. These new invertibility conditions are weaker than those considered in the current literature. This shows that the theory of time scale symplectic systems, rather than the theory of linear Hamiltonian systems, is fundamentalfor optimal control problems. Our results in this paper are new even for the Jacobi equations arising in the time scale calculus of variation and, in particular, for the discrete time calculus of variations and optimal control problems. We also show thatnonlinear time scale Hamiltonian systems possess symplectic structure, that is, the Jacobian of the evolution mapping satisfies a time scale symplectic system.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2010

Confidentiality

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

Name of the periodical

International Journal of Difference Equations

ISSN

0973-6069

e-ISSN

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Volume of the periodical

5

Issue of the periodical within the volume

1

Country of publishing house

IN - INDIA

Number of pages

27

Pages from-to

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UT code for WoS article

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EID of the result in the Scopus database

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