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Statements

Subject Item
n2:RIV%2F68407700%3A21230%2F12%3A00194283%21RIV13-GA0-21230___
rdf:type
skos:Concept n15:Vysledek
dcterms: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.
dcterms: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
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
skos:notation
RIV/68407700:21230/12:00194283!RIV13-GA0-21230___
n15:predkladatel
n16:orjk%3A21230
n3:aktivita
n7:P
n3:aktivity
P(GAP103/10/0628)
n3:cisloPeriodika
8
n3:dodaniDat
n12:2013
n3:domaciTvurceVysledku
Henrion, Didier
n3:druhVysledku
n18:J
n3:duvernostUdaju
n11:S
n3:entitaPredkladatele
n4:predkladatel
n3:idSjednocenehoVysledku
128760
n3:idVysledku
RIV/68407700:21230/12:00194283
n3:jazykVysledku
n19:eng
n3:klicovaSlova
polynomials; nonconvex optimisation; LMI; fixed-order controller design
n3:klicoveSlovo
n5:LMI n5:nonconvex%20optimisation n5:fixed-order%20controller%20design n5:polynomials
n3:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n3:kontrolniKodProRIV
[317243416FFD]
n3:nazevZdroje
International Journal of Control
n3:obor
n13:BC
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n14:GAP103%2F10%2F0628
n3:rokUplatneniVysledku
n12:2012
n3:svazekPeriodika
85
n3:tvurceVysledku
Henrion, Didier Louembet, Ch.
n3:wos
000305256900009
s:issn
0020-7179
s:numberOfPages
10
n9:doi
10.1080/00207179.2012.675521
n6:organizacniJednotka
21230