Takagi-Sugeno models in a tensor product approach: exploiting the representation

Detalhes bibliográficos
Autor(a) principal: Víctor Costa da Silva Campos
Data de Publicação: 2015
Tipo de documento: Tese
Idioma: por
Título da fonte: Repositório Institucional da UFMG
Texto Completo: http://hdl.handle.net/1843/BUBD-AX8P8J
Resumo: Takagi-Sugeno(TS) fuzzy analysis and control techniques extend several results from linear robust control theory to non linear systems. However, in many cases,the conditions used do not explore the membership functions information aside from the fact that they belong to the standard unit simplex. In addition, since we are dealing with nonlinear systems, the use of quadratic Lyapunov functions carries a certain conservatism.In this work, we propose different ways to exploit the membership functions information in parameter dependent Linear Matrix Inequalities (LMIs) as well as new classes of candidate Lyapunov functions that cover other existing classes in the literature.Asymptotically necessary conditions for parameter dependent LMIs are proposed based on partitioning the membership functions image space. Such partitions are also used to propose a switched control law and we present ways to modify the conditions of this controller such that a continuous controller can be recovered. An alternative way to reduce the number of rules of a given Takagi-Sugeno model, based on the Higher Order Singular Value Decomposition (HOSVD), is presented as well as how to model the uncertainty introduced by this rule reduction scheme. We propose the use of local transformations of the membership functions in conjunction with piece wise fuzzy Lyapunov functions so as to nd more relaxed stability conditions than others available in the literature. A novel way to deal with the time derivative of the membership functions, in cases where they are functions of the states, is proposed. This new proposition avoids the use of direct bounds over the membership functions time-derivative, and new stability and stabilization conditions are presented. Finally, we propose new LMI synthesis conditions based on piecewise-like Lyapunov functions. This class of Lyapunov functions behaves similarly to piecewise functions (in the sense that we can understand that a different function is valid for each region) while using a fuzzy formulation. By adapting recent conditions to deal with bounds on the Lyapunov functions membership functions time derivative, new synthesis conditions are presented to guarantee local stabilization
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spelling Takagi-Sugeno models in a tensor product approach: exploiting the representationEngenharia elétricaEngenharia elétricaSistemas não linearesLiapunov, Funções deTakagi-Sugeno(TS) fuzzy analysis and control techniques extend several results from linear robust control theory to non linear systems. However, in many cases,the conditions used do not explore the membership functions information aside from the fact that they belong to the standard unit simplex. In addition, since we are dealing with nonlinear systems, the use of quadratic Lyapunov functions carries a certain conservatism.In this work, we propose different ways to exploit the membership functions information in parameter dependent Linear Matrix Inequalities (LMIs) as well as new classes of candidate Lyapunov functions that cover other existing classes in the literature.Asymptotically necessary conditions for parameter dependent LMIs are proposed based on partitioning the membership functions image space. Such partitions are also used to propose a switched control law and we present ways to modify the conditions of this controller such that a continuous controller can be recovered. An alternative way to reduce the number of rules of a given Takagi-Sugeno model, based on the Higher Order Singular Value Decomposition (HOSVD), is presented as well as how to model the uncertainty introduced by this rule reduction scheme. We propose the use of local transformations of the membership functions in conjunction with piece wise fuzzy Lyapunov functions so as to nd more relaxed stability conditions than others available in the literature. A novel way to deal with the time derivative of the membership functions, in cases where they are functions of the states, is proposed. This new proposition avoids the use of direct bounds over the membership functions time-derivative, and new stability and stabilization conditions are presented. Finally, we propose new LMI synthesis conditions based on piecewise-like Lyapunov functions. This class of Lyapunov functions behaves similarly to piecewise functions (in the sense that we can understand that a different function is valid for each region) while using a fuzzy formulation. By adapting recent conditions to deal with bounds on the Lyapunov functions membership functions time derivative, new synthesis conditions are presented to guarantee local stabilizationAs técnicas de análise e controle de sistemas Takagi-Sugeno(TS) estendem vários resultados de controle robusto de sistemas lineares para sistemas não-lineares. Entretanto, em muitos dos casos, as condições utilizadas não exploram a informação das funções de pertinência do sistema, com exceção do fato de elas pertencerem ao simplex unitário padrão. Além disso, por se tratarem de sistemas não-lineares, o uso de funções de Lyapunov quadráticas carrega consigo um certo conservadorismo. Neste trabalho são propostas algumas formas diferentes de se explorar a informação das funções de pertinêncianas Desigualdades Matriciais Lineares(LMIs) dependentes de parâmetros bem como novas classes de funções de Lyapunov candidatas que cobrem outras classes existentes na literatura.São propostas condições as sintoticamente necessárias para LMIs dependentes de parâmetros baseadas em partições do espaço imagem das funções de pertinência. Tais partições são também utilizadas para se propor uma lei de controle chaveada de acordo com tais partições e como modicar as condições dessa lei de controle chaveada para que se possa recuperar um controlador contínuo. Uma maneira alternativa, baseada na Decomposição de Valores Singulares de Alta Ordem(HOSVD) para a redução do número de regras de modelos TS é proposta, bem como formas de se modelar a incerteza introduzida pelo procedimento de redução de regras proposto. É proposto o uso de transformações locais das funções de pertinência em conjunto com funções de Lyapunov fuzzy por partes de modo a se encontrar condições de estabilidade mais relaxadas do que outras apresentadas na literatura.Uma nova forma de lidar com a derivada temporal das funções de pertinência é proposta para os casos em que as funções de pertinência são funções das variáveis de estado somente. Esta nova proposição evita o uso de limitantes sobre as derivadas temporais das funções de pertinência, e novas condições de estabilidade e estabilização são apresentadas. Finalmente, são apresentadas novas condições LMI de síntese baseadas em funções de Lyapunov quase-por-partes. Esta classe de funções de Lyapunov se comporta de maneira similar às funções por partes(no sentido de que pode-se entender que uma função diferente é válida para cada região) e faz uso de uma formulação fuzzy. Adaptando-se condições recentes na literatura sobre limitantes superiores nas derivadas temporais das funções de pertinência da função de Lyapunov, novas condições desíntesesão propostas para garantir a estabilização localUniversidade Federal de Minas GeraisUFMGLeonardo Antonio Borges TorresReinaldo Martinez PalharesFernando de Oliveira SouzaRicardo Hiroshi Caldeira TakahashiEduardo Stockler TognettiEduardo Nunes GonçalvesJoão Pedro HespanhaVíctor Costa da Silva Campos2019-08-12T20:02:54Z2019-08-12T20:02:54Z2015-06-10info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisapplication/pdfhttp://hdl.handle.net/1843/BUBD-AX8P8Jinfo:eu-repo/semantics/openAccessporreponame:Repositório Institucional da UFMGinstname:Universidade Federal de Minas Gerais (UFMG)instacron:UFMG2019-11-14T22:46:02Zoai:repositorio.ufmg.br:1843/BUBD-AX8P8JRepositório InstitucionalPUBhttps://repositorio.ufmg.br/oairepositorio@ufmg.bropendoar:2019-11-14T22:46:02Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)false
dc.title.none.fl_str_mv Takagi-Sugeno models in a tensor product approach: exploiting the representation
title Takagi-Sugeno models in a tensor product approach: exploiting the representation
spellingShingle Takagi-Sugeno models in a tensor product approach: exploiting the representation
Víctor Costa da Silva Campos
Engenharia elétrica
Engenharia elétrica
Sistemas não lineares
Liapunov, Funções de
title_short Takagi-Sugeno models in a tensor product approach: exploiting the representation
title_full Takagi-Sugeno models in a tensor product approach: exploiting the representation
title_fullStr Takagi-Sugeno models in a tensor product approach: exploiting the representation
title_full_unstemmed Takagi-Sugeno models in a tensor product approach: exploiting the representation
title_sort Takagi-Sugeno models in a tensor product approach: exploiting the representation
author Víctor Costa da Silva Campos
author_facet Víctor Costa da Silva Campos
author_role author
dc.contributor.none.fl_str_mv Leonardo Antonio Borges Torres
Reinaldo Martinez Palhares
Fernando de Oliveira Souza
Ricardo Hiroshi Caldeira Takahashi
Eduardo Stockler Tognetti
Eduardo Nunes Gonçalves
João Pedro Hespanha
dc.contributor.author.fl_str_mv Víctor Costa da Silva Campos
dc.subject.por.fl_str_mv Engenharia elétrica
Engenharia elétrica
Sistemas não lineares
Liapunov, Funções de
topic Engenharia elétrica
Engenharia elétrica
Sistemas não lineares
Liapunov, Funções de
description Takagi-Sugeno(TS) fuzzy analysis and control techniques extend several results from linear robust control theory to non linear systems. However, in many cases,the conditions used do not explore the membership functions information aside from the fact that they belong to the standard unit simplex. In addition, since we are dealing with nonlinear systems, the use of quadratic Lyapunov functions carries a certain conservatism.In this work, we propose different ways to exploit the membership functions information in parameter dependent Linear Matrix Inequalities (LMIs) as well as new classes of candidate Lyapunov functions that cover other existing classes in the literature.Asymptotically necessary conditions for parameter dependent LMIs are proposed based on partitioning the membership functions image space. Such partitions are also used to propose a switched control law and we present ways to modify the conditions of this controller such that a continuous controller can be recovered. An alternative way to reduce the number of rules of a given Takagi-Sugeno model, based on the Higher Order Singular Value Decomposition (HOSVD), is presented as well as how to model the uncertainty introduced by this rule reduction scheme. We propose the use of local transformations of the membership functions in conjunction with piece wise fuzzy Lyapunov functions so as to nd more relaxed stability conditions than others available in the literature. A novel way to deal with the time derivative of the membership functions, in cases where they are functions of the states, is proposed. This new proposition avoids the use of direct bounds over the membership functions time-derivative, and new stability and stabilization conditions are presented. Finally, we propose new LMI synthesis conditions based on piecewise-like Lyapunov functions. This class of Lyapunov functions behaves similarly to piecewise functions (in the sense that we can understand that a different function is valid for each region) while using a fuzzy formulation. By adapting recent conditions to deal with bounds on the Lyapunov functions membership functions time derivative, new synthesis conditions are presented to guarantee local stabilization
publishDate 2015
dc.date.none.fl_str_mv 2015-06-10
2019-08-12T20:02:54Z
2019-08-12T20:02:54Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/doctoralThesis
format doctoralThesis
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/1843/BUBD-AX8P8J
url http://hdl.handle.net/1843/BUBD-AX8P8J
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal de Minas Gerais
UFMG
publisher.none.fl_str_mv Universidade Federal de Minas Gerais
UFMG
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFMG
instname:Universidade Federal de Minas Gerais (UFMG)
instacron:UFMG
instname_str Universidade Federal de Minas Gerais (UFMG)
instacron_str UFMG
institution UFMG
reponame_str Repositório Institucional da UFMG
collection Repositório Institucional da UFMG
repository.name.fl_str_mv Repositório Institucional da UFMG - Universidade Federal de Minas Gerais (UFMG)
repository.mail.fl_str_mv repositorio@ufmg.br
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