Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F12%3A00194283" target="_blank" >RIV/68407700:21230/12:00194283 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1080/00207179.2012.675521" target="_blank" >http://dx.doi.org/10.1080/00207179.2012.675521</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1080/00207179.2012.675521" target="_blank" >10.1080/00207179.2012.675521</a>
Alternative languages
Result language
angličtina
Original language name
Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design
Original language 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 canbe used to design fixed-order controllers for linear systems, following a polynomial approach.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BC - Theory and management systems
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GAP103%2F10%2F0628" target="_blank" >GAP103/10/0628: Semidefinite programming for nonlinear dynamical systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Control
ISSN
0020-7179
e-ISSN
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Volume of the periodical
85
Issue of the periodical within the volume
8
Country of publishing house
GB - UNITED KINGDOM
Number of pages
10
Pages from-to
1083-1092
UT code for WoS article
000305256900009
EID of the result in the Scopus database
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