Conditions of output stabilization for nonlinear models in the Takagi–Sugeno's form

Guerra, Thierry Marie; Kruszewski, Alexandre; Vermeiren, Laurent; Tirmant, Hélène

doi:10.1016/j.fss.2005.12.006

Cited by 251 publications

(113 citation statements)

References 18 publications

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“…Note that, in the presented results the system model do not include stability conditions of output stabilization for uncertain fuzzy models. This has been reported in (Guerra, Kruszewski, Vermeiren, & Tirmant, 2006). …”

Section: Stabilization Designsupporting

confidence: 61%

Relaxed LMI conditions for control of nonlinear Takagi-Sugeno models

Latorre¹,

Vicente²

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RESUMENLos problemas de optimización de desigualdades matriciales lineales en control borroso se han convertido en la herramienta más utilizada en dichaárea desde los años 90. Muchos sistemas no lineales pueden ser modelados como sistemas borrosos de modo que el control borroso puede considerarse como una técnica de control no lineal. Aunque se han obtenido muchos y buenos resultados, quedan algunas fuentes de conservadurismo cuando se comparan con otros enfoques de control no lineal. Esta tesis discute dichas cuestiones de conservadurismo y plantea nuevos enfoques para resolverlas.La principal ventaja de la formulación mediante desigualdades matriciales lineales es la posibilidad de asegurar estabilidad y prestaciones de un sistema no lineal modelado como un sistema borroso TakagiSugeno. Estos modelos están formados por un conjunto de modelos lineales eligiendo el sistema a aplicar mediante el uso de unas reglas borrosas. Estas reglas se traducen en funciones de interpolación o de pertenecía que nos indican el grado de validez de un modelo lineal respecto del resto. El mayor problema que presentan estas técnicas basadas en desigualdades matriciales lineales es que las funciones de pertenencia no están incluidas en las condiciones de estabilidad del sistema, lo que significa que se prueba la estabilidad y prestaciones para cualquier forma de interpolación entre los diferentes modelos lineales. Esto genera una fuente de conservadurismo que sería conveniente limitar.En la tesis doctoral se presentan varias metodologías capaces de trasladar la información de las funciones de pertenencia del sistema al problema basado en desigualdades matriciales lineales de estabilidad y prestaciones. Las dos principales aportaciones propuestas se basan, respectivamente, en introducir una serie de matrices de relajación que periii iv mitan incorporar esta información y en aprovechar la descripción de una amplia clase de sistemas borrosos en productos tensoriales de modelos lineales, en los que cada función de pertenencia se obtiene del producto cartesiano de varias funciones.Por otro lado, el problema de estabilidad y prestaciones para sistemas borrosos Takagi-Sugeno está basado en las condiciones de estabilidad de Lyapunov y no resulta equivalente al problema en desigualdades matriciales lineales obtenido, siendo esteúltimo conservativo respecto al primero. Así una de las mayores aportaciones de la tesis es la introducción de nuevas condiciones de estabilidad y prestaciones que mediante un parámetro de diseño permiten acercar esta equivalencia entre las expresiones, resultando equivalentes asintóticamente con el aumento del parámetro. Como inconveniente, el aumento del parámetro comporta un aumento en la complejidad del problema a resolver. RESUMEls problemes d'optimització de desigualtats matricials lineals en control borrós s'han convertit en la ferramenta més utilitzada a l'àrea des dels anys 90. Molts sistemes no lineals poden ser modelats com sistemes borrosos, de tal forma que el control borrós es pot considerar com una tècn...

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Section: Stabilization Designsupporting

confidence: 61%

Relaxed LMI conditions for control of nonlinear Takagi-Sugeno models

Latorre¹,

Vicente²

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“…. , U T N −1 ) T and G γ,k is formulated by extracting out x 0 and U from Ξ γ in (34), in order to express (33) in matrix form (36).…”

Section: Resultsmentioning

confidence: 99%

“…Our terminal controller even for the same level of Polya complexity parameter will, hence, prove a better cost bound. Note, however, that they consider uncertainty in the TS vertex models as well as persistent disturbances so such conservative steps are clearly justified and needed to synthesise the terminal controller; on the other hand, our approach purposely does not consider uncertain models, although incorporating polytopic uncertainty such as that in [36] is indeed possible, by omitting dependence of the controller parametrisation (23) on unknown components; if not component were known, our control actions would be the plain scalars in minimax predictive control [19].…”

Section: Discussion and Comparative Analysismentioning

confidence: 99%

“…Note that, if memberships are considered as "uncertainty" and the controller cannot depend on them, the above problem statement would be that of the so-called minimax predictive control [18,19]. Intermediate cases with partiallyknown membership components [36,Eq. (27)], may also be conceived, but they will be left out of the scope of the discussion for brevity.…”

Section: Remarkmentioning

confidence: 99%

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Shape-independent model predictive control for Takagi–Sugeno fuzzy systems

Ariño

Querol

Sala³

2017

Engineering Applications of Artificial Intelligence

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Predictive control of TS fuzzy systems has been addressed in prior literature with some simplifying assumptions or heuristic approaches. This paper presents a rigorous formulation of the model predictive control of TS systems, so that results are valid for any membership value (shape-independent) with a suitable account of causality (control can depend on current and past memberships and state). As in most fuzzy control results, a family of progressively better controllers can be obtained by increasing Polya-related complexity parameters, generalising over prior proposals.

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“…The main advantage of these models is the ability to extend the tools designed in the linear system framework. Indeed, many topics of control are extended to TS systems, such as stability and stabilization in Tanaka et al [1998], Guerra et al [2006], Chadli et al [2002], observers and state estimation in Akhenak et al [2007], Bergsten et al [2002].…”

Section: Introductionmentioning

confidence: 99%

Fault diagnosis for Takagi-Sugeno nonlinear systems

Ichalal

Marx

Ragot

et al. 2009

IFAC Proceedings Volumes

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This paper addresses a new scheme for fault diagnosis in nonlinear systems described by Takagi-Sugeno multiple models. Two cases are considered, the first one concerns the T-S models with known premise variables (the input or the output of the system). For the second case it is supposed that the weighting functions depend on unmeasurable premise variables (state of the system). The approach is based on the design of observer-based residual generator by minimization of the disturbances effect and maximizing the effects of the faults. The synthesis is based on the L 2 formalism developed for linear systems. The convergence conditions are given in LMI formulation.

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Conditions of output stabilization for nonlinear models in the Takagi–Sugeno's form

Cited by 251 publications

References 18 publications

Relaxed LMI conditions for control of nonlinear Takagi-Sugeno models

Relaxed LMI conditions for control of nonlinear Takagi-Sugeno models

Shape-independent model predictive control for Takagi–Sugeno fuzzy systems

Fault diagnosis for Takagi-Sugeno nonlinear systems

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