About: Measures and LMIs for Impulsive Nonlinear Optimal Control

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	This note shows how to use semi-definite programming to find lower bounds on a large class of nonlinear optimal control problems with polynomial dynamics and convex semialgebraic state constraints and an affine dependence on the control. This is done by relaxing an optimal control problem into a linear programming problem on measures, also known as a generalized moment problem. The handling of measures by their moments reduces the problem to a convergent series of standard linear matrix inequality relaxations. When the optimal control consists of a finite number of impulses, we can recover simultaneously the actual impulse times and amplitudes by simple linear algebra. Finally, our approach can be readily implemented with standard software, as illustrated by a numerical example. This note shows how to use semi-definite programming to find lower bounds on a large class of nonlinear optimal control problems with polynomial dynamics and convex semialgebraic state constraints and an affine dependence on the control. This is done by relaxing an optimal control problem into a linear programming problem on measures, also known as a generalized moment problem. The handling of measures by their moments reduces the problem to a convergent series of standard linear matrix inequality relaxations. When the optimal control consists of a finite number of impulses, we can recover simultaneously the actual impulse times and amplitudes by simple linear algebra. Finally, our approach can be readily implemented with standard software, as illustrated by a numerical example. (en)
Title	Measures and LMIs for Impulsive Nonlinear Optimal Control Measures and LMIs for Impulsive Nonlinear Optimal Control (en)
skos:prefLabel	Measures and LMIs for Impulsive Nonlinear Optimal Control Measures and LMIs for Impulsive Nonlinear Optimal Control (en)
skos:notation	RIV/68407700:21230/14:00217550!RIV15-MSM-21230___
http://linked.open...avai/riv/aktivita	I
http://linked.open...avai/riv/aktivity	I
http://linked.open...iv/cisloPeriodika	5
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Henrion, Didier
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	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	27975
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/14:00217550
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Impulsive control; linear matrix inequalities; moment approach; occupation measures; optimal control (en)
http://linked.open.../riv/klicoveSlovo	linear matrix inequalities optimal control occupation measures Impulsive control moment approach
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[01CFD9B13AD3]
http://linked.open...i/riv/nazevZdroje	IEEE Transactions on Automatic Control
http://linked.open...in/vavai/riv/obor	BC
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	4 (xsd:int)
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	59
http://linked.open...iv/tvurceVysledku	Henrion, Didier Arzelier, D. Lasserre, J. B. Claeys, M.
http://linked.open...ain/vavai/riv/wos	000335218900027
issn	0018-9286
number of pages	6 (xsd:int)
http://bibframe.org/vocab/doi	10.1109/TAC.2013.2292735
http://localhost/t...ganizacniJednotka	21230

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