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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F11%3A00185249" target="_blank" >RIV/68407700:21230/11:00185249 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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 werecall 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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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 werecall 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.

Druh

O - Ostatní výsledky

CEP obor

BC - Teorie a systémy řízení

OECD FORD obor

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Projekt

<a href="/cs/project/GAP103%2F10%2F0628" target="_blank" >GAP103/10/0628: Semidefinitní programování po nelineární dynamické systémy</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2011

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů