Discrete optimal control: second order optimality conditions

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F02%3A00008170" target="_blank" >RIV/00216224:14310/02:00008170 - 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

Discrete optimal control: second order optimality conditions

Original language description

In this paper we present a survey and refinement of our recent results in the discrete optimal control theory. For a general nonlinear discrete optimal control problem (P), second order necessary and sufficient optimality conditions are derived via the nonnegativity (<i> I&gt;=0 </i>) and positivity (<i> I&gt;0 </i>) of the discrete quadratic functional <i> I </i> corresponding to its second variation. Thus, we fill the gap in the discrete-time theory by connecting the discrete control problems with thetheory of conjugate intervals, Hamiltonian systems, and Riccati equations. Necessary conditions for <i> I&gt;=0 </i> are formulated in terms of the positivity of certain partial discrete quadratic functionals, the nonexistence of conjugate intervals, the existence of conjoined bases of the associated linear Hamiltonian system, and the existence of solutions to Riccati matrix equations. Natural strengthening of each of these conditions yields a characterization of the positivity of <i> I

Czech name

Discrete optimal control: second order optimality conditions

Czech description

In this paper we present a survey and refinement of our recent results in the discrete optimal control theory. For a general nonlinear discrete optimal control problem (P), second order necessary and sufficient optimality conditions are derived via the nonnegativity (<i> I&gt;=0 </i>) and positivity (<i> I&gt;0 </i>) of the discrete quadratic functional <i> I </i> corresponding to its second variation. Thus, we fill the gap in the discrete-time theory by connecting the discrete control problems with thetheory of conjugate intervals, Hamiltonian systems, and Riccati equations. Necessary conditions for <i> I&gt;=0 </i> are formulated in terms of the positivity of certain partial discrete quadratic functionals, the nonexistence of conjugate intervals, the existence of conjoined bases of the associated linear Hamiltonian system, and the existence of solutions to Riccati matrix equations. Natural strengthening of each of these conditions yields a characterization of the positivity of <i> I

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

<a href="/en/project/GA201%2F01%2F0079" target="_blank" >GA201/01/0079: Qualitative theory of solutions of difference equations</a><br>

Continuities

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

Publication year

2002

Confidentiality

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

Name of the periodical

Journal of Difference Equations and Applications

ISSN

1023-6198

e-ISSN

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Volume of the periodical

8

Issue of the periodical within the volume

10

Country of publishing house

GB - UNITED KINGDOM

Number of pages

22

Pages from-to

875-896

UT code for WoS article

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EID of the result in the Scopus database

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