. . "21230" . . "Henrion, Didier" . . . "000305256900009" . "10.1080/00207179.2012.675521" . "[317243416FFD]" . "Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design" . "2"^^ . . . "1"^^ . "Henrion, Didier" . "128760" . "Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design" . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . . "Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design"@en . "Convex inner approximations of nonconvex semialgebraic sets applied to fixed-order controller design"@en . "International Journal of Control" . . "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." . "85" . . . "Louembet, Ch." . "RIV/68407700:21230/12:00194283!RIV13-GA0-21230___" . . "P(GAP103/10/0628)" . "10"^^ . "polynomials; nonconvex optimisation; LMI; fixed-order controller design"@en . . "8" . . "0020-7179" . . "RIV/68407700:21230/12:00194283" . "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 . .