Estimaación del dominio de atracción de sistemas no lineales mediante modelos borrosos polinomiales

Pitarch, J.L.; Sala, A.; Ariño, C.V.; Bedate, F.

doi:10.1016/j.riai.2012.02.007

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Resumen

La mayor parte de referencias de la literatura en control borroso plantean condiciones LMI para un modelo Takagi-Sugeno y dan por terminado el problema una vez se obtienen resultados factibles. No obstante, dejan sin estudiar la región de atracción obtenida. Este tra-baajo propone probar que una zona, de forma prefijada, lo más grande posible, peertenece al dominio de atracción del origen de un sistema no lineal. Para ello, se usan modelos borrosos polinomiales cuyo análisis puede ser llevado a cabo mediante optimización convexa (su-mas de cuadrados). Asimismo, se utiliza información de la forma de las funciones de pertenencia para realizar iteraciones con la región de modelado borroso, maximizando la región de atracción probada, lo cual reduce el conservadurismo sobre otras propuestas.

Palabras clave:

Función de Lyapunov

dominio de atracción

sistemas borrosos

Takagi-Sugeno

sistemas polinomiales

estabilidad local

sumas de cuadrados

conservadurismo

Abstract

Many approaches in fuzzy systems literature express LMI conditions for a Takagi-Sugeno model and finish the problem once those conditions are feasible. However, studying the obtained region of attraction and its relationship with the original nonlinear problem is forgotten. This paper proposes to obtain a predefined-shape zone, as large as possible, belonging to the local domain of attraction of the origin of a nonlinear system. In order to do this, local fuzzy polynomial models are used whose analysis can be carried out by convex optimization (sum of squares). Moreover membership information is used in order to do iterations with the fuzzy modeling region, maximizing the size of the proven domain of attraction, which reduces conservatism over existing results.

Keywords:

Lyapunov function

domain of attracion

fuzzy systems

Takagi-Sugeno

polinomial systems

local stabilty

sum of squares

conservatism

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Referencias no citadas

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