About: Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Using Hermite's formulation of polynomial stability conditions, static output feedback (SOF) controller design can be formulated as a polynomial matrix inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming problem that can be solved (locally) with PENNON, an implementation of a penalty and augmented Lagrangian method. Typically, Hermite SOF PMI problems are badly scaled and experiments reveal that this has a negative impact on the overall performance of the solver. In this note we recall the algebraic interpretation of Hermite's quadratic form as a particular Bezoutian and we use results on polynomial interpolation to express the Hermite PMI in a Lagrange polynomial basis, as an alternative to the conventional power basis. Numerical experi- ments on benchmark problem instances show the substantial improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behavior of PENNON. Using Hermite's formulation of polynomial stability conditions, static output feedback (SOF) controller design can be formulated as a polynomial matrix inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming problem that can be solved (locally) with PENNON, an implementation of a penalty and augmented Lagrangian method. Typically, Hermite SOF PMI problems are badly scaled and experiments reveal that this has a negative impact on the overall performance of the solver. In this note we recall the algebraic interpretation of Hermite's quadratic form as a particular Bezoutian and we use results on polynomial interpolation to express the Hermite PMI in a Lagrange polynomial basis, as an alternative to the conventional power basis. Numerical experi- ments on benchmark problem instances show the substantial improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behavior of PENNON. (en)
Title	Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities (en)
skos:prefLabel	Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities (en)
skos:notation	RIV/68407700:21230/11:00185249!RIV12-GA0-21230___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GAP103/10/0628)
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Henrion, Didier
http://linked.open.../riv/druhVysledku	O - Ostatní výsledky nezařaditelné do žádného z výše uvedených druhů výsledku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta elektrotechnická
http://linked.open...dnocenehoVysledku	201921
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/11:00185249
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Static output feedback; Hermite stability criterion; Polynomial matrix inequality; Nonlinear semidefinite programming (en)
http://linked.open.../riv/klicoveSlovo	Hermite stability criterion Nonlinear semidefinite programming Polynomial matrix inequality Static output feedback
http://linked.open...ontrolniKodProRIV	[C2B5CF38893E]
http://linked.open...in/vavai/riv/obor	BC
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Semidefinite programming for nonlinear dynamical systems
http://linked.open...UplatneniVysledku	2011
http://linked.open...iv/tvurceVysledku	Henrion, Didier Delibasi, A.
http://localhost/t...ganizacniJednotka	21230

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