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  • 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
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GAP103/10/0628)
http://linked.open...iv/cisloPeriodika
  • 8
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
  • Henrion, Didier
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 128760
http://linked.open...ai/riv/idVysledku
  • RIV/68407700:21230/12:00194283
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • polynomials; nonconvex optimisation; LMI; fixed-order controller design (en)
http://linked.open.../riv/klicoveSlovo
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
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
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
http://bibframe.org/vocab/doi
  • 10.1080/00207179.2012.675521
http://localhost/t...ganizacniJednotka
  • 21230
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