Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F12%3A00057199" target="_blank" >RIV/00216224:14310/12:00057199 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.na.2011.09.027" target="_blank" >http://dx.doi.org/10.1016/j.na.2011.09.027</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.na.2011.09.027" target="_blank" >10.1016/j.na.2011.09.027</a>
Alternative languages
Result language
angličtina
Original language name
Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems
Original language description
In this paper we first derive the verification theorem for nonlinear optimal control problems over time scales. That is, we show that the value function is the only solution of the Hamilton-Jacobi equation, in which the minimum is attained at an optimalfeedback controller. Applications to the linear-quadratic regulator problem (LQR problem) gives a feedback optimal controller form in terms of the solution of a generalized time scale Riccati equation, and that every optimal solution of the LQR problem must take that form. A connection of the newly obtained Riccati equation with the traditional one is established. Problems with shift in the state variable are also considered. As an important tool for the latter theory we obtain a new formula for the chain rule on time scales. Finally, the corresponding LQR problem with shift in the state variable is analyzed and the results are related to previous ones.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
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)
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nonlinear Analysis, Theory, Methods & Applications
ISSN
0362-546X
e-ISSN
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Volume of the periodical
75
Issue of the periodical within the volume
2
Country of publishing house
GB - UNITED KINGDOM
Number of pages
19
Pages from-to
932-950
UT code for WoS article
000296562200040
EID of the result in the Scopus database
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