Mathematics > Optimization and Control
[Submitted on 14 Apr 2011 (v1), last revised 10 Jan 2012 (this version, v2)]
Title:Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design
View PDFAbstract: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 regions with concave boundaries. In particular, the algorithm leaves invariant a given convex set. The algorithm is based on Gloptipoly 3, a public-domain Matlab package solving nonconvex polynomial optimization problems with the help of convex semidefinite programming (optimization 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.
Submission history
From: Didier Henrion [view email] [via CCSD proxy][v1] Thu, 14 Apr 2011 07:00:33 UTC (196 KB)
[v2] Tue, 10 Jan 2012 20:16:33 UTC (217 KB)
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