About: Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design

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Description	We describe an elementary algorithm to build convex inner approximations of nonconvex sets. Both input and output sets are basic semialgebraic sets given as lists of defining multivariate polynomials. Even though no optimality guarantees can be given (e.g. in terms of volume maximisation for bounded sets), the algorithm is designed to preserve convex boundaries as much as possible, while removing regions with concave boundaries. In particular, the algorithm leaves invariant a given convex set. The algorithm is based on Gloptipoly 3, a publicdomain Matlab package solving nonconvex polynomial optimisation problems with the help of convex semidefinite programming (optimisation over linear matrix inequalities, or LMIs). We illustrate how the algorithm can be used to design fixed-order controllers for linear systems, following a polynomial approach. We describe an elementary algorithm to build convex inner approximations of nonconvex sets. Both input and output sets are basic semialgebraic sets given as lists of defining multivariate polynomials. Even though no optimality guarantees can be given (e.g. in terms of volume maximisation for bounded sets), the algorithm is designed to preserve convex boundaries as much as possible, while removing regions with concave boundaries. In particular, the algorithm leaves invariant a given convex set. The algorithm is based on Gloptipoly 3, a publicdomain Matlab package solving nonconvex polynomial optimisation problems with the help of convex semidefinite programming (optimisation over linear matrix inequalities, or LMIs). We illustrate how the algorithm can be used to design fixed-order controllers for linear systems, following a polynomial approach. (en)
Title	Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design (en)
skos:prefLabel	Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design (en)
skos:notation	RIV/68407700:21230/12:00194283!RIV13-GA0-21230___
http://linked.open...avai/predkladatel	Fakulta elektrotechnická
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GAP103/10/0628)
http://linked.open...iv/cisloPeriodika	8
http://linked.open...vai/riv/dodaniDat	2013
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	128760
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/12:00194283
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	polynomials; nonconvex optimisation; LMI; fixed-order controller design (en)
http://linked.open.../riv/klicoveSlovo	LMI nonconvex optimisation polynomials fixed-order controller design
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[317243416FFD]
http://linked.open...i/riv/nazevZdroje	International Journal of Control
http://linked.open...in/vavai/riv/obor	BC
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Semidefinite programming for nonlinear dynamical systems
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	85
http://linked.open...iv/tvurceVysledku	Henrion, Didier Louembet, Ch.
http://linked.open...ain/vavai/riv/wos	000305256900009
issn	0020-7179
number of pages	10 (xsd:int)
http://bibframe.org/vocab/doi	10.1080/00207179.2012.675521
http://localhost/t...ganizacniJednotka	21230
is http://linked.open...avai/riv/vysledek of	Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design

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