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

Result code in IS VaVaI
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Result on the web
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DOI - Digital Object Identifier
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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 maximization for bounded sets), the algorithm is designed to preserve convex boundaries as much as possible, while removing re- gions with concave boundaries. In particular, the algorithm leaves invariant a given convex set. The algorithm is based on Gloptipoly 3, a public-domain Matlab pack- age solving nonconvex polynomial optimization problems with the help of convex semidefinite programming (optimization over linear matrix inequalities, or LMIs). We illustrate how the algorithmcan be 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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Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems - MTNS 2010
ISBN
978-963-311-370-7
ISSN
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e-ISSN
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Number of pages
14
Pages from-to
1-14
Publisher name
MTA SZTAKI - Hungarian Academy of Sciences
Place of publication
Budapest
Event location
Budapešť
Event date
Jul 5, 2010
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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