About: Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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 optimal feedback 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. 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 optimal feedback 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. (en)
Title	Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems (en)
skos:prefLabel	Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems (en)
skos:notation	RIV/00216224:14310/12:00057199!RIV13-GA0-14310___
http://linked.open...avai/predkladatel	Přírodovědecká fakulta
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	2
http://linked.open...vai/riv/dodaniDat	2013
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	138599
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/12:00057199
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Hamilton-Jacobi theory; Verification theorem; Bellman principle; Dynamic programming; Hamilton-Jacobi-Bellman equation; Value function; Linear-quadratic problem; Riccati equation; Feedback controller; Symplectic system; Weak Pontryagin principle (en)
http://linked.open.../riv/klicoveSlovo	Weak Pontryagin principle Riccati equation Value function Bellman principle Feedback controller Hamilton-Jacobi-Bellman equation Linear-quadratic problem Symplectic system Verification theorem Hamilton-Jacobi theory Dynamic programming
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[C3082FCAA3CE]
http://linked.open...i/riv/nazevZdroje	Nonlinear Analysis, Theory, Methods & 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	2012
http://linked.open...v/svazekPeriodika	75
http://linked.open...iv/tvurceVysledku	Zeidan, Vera Michel Šimon Hilscher, Roman
http://linked.open...ain/vavai/riv/wos	000296562200040
http://linked.open...n/vavai/riv/zamer	Matematické struktury a jejich fyzikální aplikace
issn	0362-546X
number of pages	19 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.na.2011.09.027
http://localhost/t...ganizacniJednotka	14310
is http://linked.open...avai/riv/vysledek of	Hamilton-Jacobi theory over time scales and applications to linear-quadratic problems

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