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 Be´zoutian 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 experiments on benchmark problem instances show the improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behaviour 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 Be´zoutian 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 experiments on benchmark problem instances show the improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behaviour 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/68407700:21230/10:00172903!RIV11-GA0-21230___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GAP103/10/0628), Z(MSM6840770038)
http://linked.open...iv/cisloPeriodika	12
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Henrion, Didier
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
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	261428
http://linked.open...ai/riv/idVysledku	RIV/68407700:21230/10:00172903
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	static output feedback; Hermite stability criterion; polynomial matrix inequality; nonlinear (en)
http://linked.open.../riv/klicoveSlovo	nonlinear polynomial matrix inequality Hermite stability criterion static output feedback
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[F6DB64CD4FCC]
http://linked.open...i/riv/nazevZdroje	International Journal of Control
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	2010
http://linked.open...v/svazekPeriodika	83
http://linked.open...iv/tvurceVysledku	Henrion, Didier Delibaşı, A.
http://linked.open...ain/vavai/riv/wos	000285354700008
http://linked.open...n/vavai/riv/zamer	Decision Making and Control for Manufacturing III
issn	0020-7179
number of pages	12 (xsd:int)
http://localhost/t...ganizacniJednotka	21230

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