Inner Approximations for Polynomial Matrix Inequalities and Robust Stability Regions

Kód výsledku v IS VaVaI

RIV/68407700:21230/12:00193378 - isvavai.cz

Výsledek na webu

http://dx.doi.org/10.1109/TAC.2011.2178717

DOI - Digital Object Identifier

10.1109/TAC.2011.2178717

Jazyk výsledku

angličtina

Název v původním jazyce

Inner Approximations for Polynomial Matrix Inequalities and Robust Stability Regions

Popis výsledku v původním jazyce

Following a polynomial approach, many robust fixedorder controller design problems can be formulated as optimization problems whose set of feasible solutions is modeled by parametrized polynomial matrix inequalities (PMIs). These feasibility sets are typically nonconvex. Given a parametrized PMI set, we provide a hierarchy of linear matrix inequality (LMI) problems whose optimal solutions generate inner approximations modeled by a single polynomial superlevel set. Those inner approximations converge ina well-defined analytic sense to the nonconvex original feasible set, with asymptotically vanishing conservatism. One may also impose the hierarchy of inner approximations to be nested or convex. In the latter case, they do not converge any more to the feasible set, but they can be used in a convex optimization framework at the price of some conservatism. Finally, we show that the specific geometry of nonconvex polynomial stability regions can be exploited to improve convergence of the h

Název v anglickém jazyce

Inner Approximations for Polynomial Matrix Inequalities and Robust Stability Regions

Popis výsledku anglicky

Following a polynomial approach, many robust fixedorder controller design problems can be formulated as optimization problems whose set of feasible solutions is modeled by parametrized polynomial matrix inequalities (PMIs). These feasibility sets are typically nonconvex. Given a parametrized PMI set, we provide a hierarchy of linear matrix inequality (LMI) problems whose optimal solutions generate inner approximations modeled by a single polynomial superlevel set. Those inner approximations converge ina well-defined analytic sense to the nonconvex original feasible set, with asymptotically vanishing conservatism. One may also impose the hierarchy of inner approximations to be nested or convex. In the latter case, they do not converge any more to the feasible set, but they can be used in a convex optimization framework at the price of some conservatism. Finally, we show that the specific geometry of nonconvex polynomial stability regions can be exploited to improve convergence of the h

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BC - Teorie a systémy řízení

OECD FORD obor

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Projekt

GAP103/10/0628: Semidefinitní programování po nelineární dynamické systémy

Návaznosti

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

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

IEEE Transactions on Automatic Control

ISSN

0018-9286

e-ISSN

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Svazek periodika

57

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

12

Strana od-do

1456-1467

Kód UT WoS článku

000304609300009

EID výsledku v databázi Scopus

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