Relaxed Stabilization Conditions for TS Fuzzy Systems with Optimal Upper Bounds for the Time Derivative of Fuzzy Lyapunov Functions
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1109/ACCESS.2021.3076030 http://hdl.handle.net/11449/207673 |
Resumo: | This paper initially proposes an optimization problem and after presents its optimal solution. Then, this result is applied to obtain relaxed conditions to design controllers for nonlinear plants described by Takagi-Sugeno (TS) models, based on fuzzy Lyapunov function (FLF) and Linear Matrix Inequalities (LMI). The FLF is given by V(x(t)) = x(t)TP(α (x(t)))x(t), where x(t) is the plant state vector, P(α (x(t))) = α 1(x(t))P1 + α 2(x(t))P2 + c + α r(x(t))Pr, Pi=PiT > 0 and α i(x(t)) is the weight related to the local model i in the representation of the plant by TS fuzzy models, for i=1,2,c,r. When one calculates the time derivative of this V(x(t)), it appears the term x(t)T P(α (x(t)))x(t), that is usually handled using conservative upper bounds, supposing that the bounds of the time derivative of α i(x(t)), i=1,2,c,r, are available. The main result of this paper is a procedure to obtain optimal upper bounds for the term x(t)T P(α (x(t)))x(t), such that they contemplate the maximum value and are always smaller than or equal to the maximum value. It is a relevant result on this subject, because these optimal upper bounds do not add any constraint. With these optimal upper bounds, a relaxed design method for stabilization of TS fuzzy models is proposed. Two numerical examples illustrate the effectiveness of this procedure. |
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Relaxed Stabilization Conditions for TS Fuzzy Systems with Optimal Upper Bounds for the Time Derivative of Fuzzy Lyapunov Functionsfuzzy controlFuzzy Lyapunov function (FLF)linear matrix inequalities (LMIs)stabilitystabilizationTakagi-Sugeno (TS) fuzzy systemsThis paper initially proposes an optimization problem and after presents its optimal solution. Then, this result is applied to obtain relaxed conditions to design controllers for nonlinear plants described by Takagi-Sugeno (TS) models, based on fuzzy Lyapunov function (FLF) and Linear Matrix Inequalities (LMI). The FLF is given by V(x(t)) = x(t)TP(α (x(t)))x(t), where x(t) is the plant state vector, P(α (x(t))) = α 1(x(t))P1 + α 2(x(t))P2 + c + α r(x(t))Pr, Pi=PiT > 0 and α i(x(t)) is the weight related to the local model i in the representation of the plant by TS fuzzy models, for i=1,2,c,r. When one calculates the time derivative of this V(x(t)), it appears the term x(t)T P(α (x(t)))x(t), that is usually handled using conservative upper bounds, supposing that the bounds of the time derivative of α i(x(t)), i=1,2,c,r, are available. The main result of this paper is a procedure to obtain optimal upper bounds for the term x(t)T P(α (x(t)))x(t), such that they contemplate the maximum value and are always smaller than or equal to the maximum value. It is a relevant result on this subject, because these optimal upper bounds do not add any constraint. With these optimal upper bounds, a relaxed design method for stabilization of TS fuzzy models is proposed. Two numerical examples illustrate the effectiveness of this procedure.Department of Electrical Engineering Faculty of Engineering of Ilha Solteira São Paulo State University (UNESP)Department of Electrical Engineering Faculty of Engineering of Ilha Solteira São Paulo State University (UNESP)Universidade Estadual Paulista (Unesp)Lazarini, Adalberto Z. N. [UNESP]Teixeira, Marcelo C. M. [UNESP]De S. Ribeiro, Jean M. [UNESP]Assuncao, Edvaldo [UNESP]Cardim, Rodrigo [UNESP]Buzetti, Ariel S. [UNESP]2021-06-25T10:59:04Z2021-06-25T10:59:04Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article64945-64957http://dx.doi.org/10.1109/ACCESS.2021.3076030IEEE Access, v. 9, p. 64945-64957.2169-3536http://hdl.handle.net/11449/20767310.1109/ACCESS.2021.30760302-s2.0-85105044353Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengIEEE Accessinfo:eu-repo/semantics/openAccess2024-07-04T19:06:13Zoai:repositorio.unesp.br:11449/207673Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T17:28:47.773514Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Relaxed Stabilization Conditions for TS Fuzzy Systems with Optimal Upper Bounds for the Time Derivative of Fuzzy Lyapunov Functions |
title |
Relaxed Stabilization Conditions for TS Fuzzy Systems with Optimal Upper Bounds for the Time Derivative of Fuzzy Lyapunov Functions |
spellingShingle |
Relaxed Stabilization Conditions for TS Fuzzy Systems with Optimal Upper Bounds for the Time Derivative of Fuzzy Lyapunov Functions Lazarini, Adalberto Z. N. [UNESP] fuzzy control Fuzzy Lyapunov function (FLF) linear matrix inequalities (LMIs) stability stabilization Takagi-Sugeno (TS) fuzzy systems |
title_short |
Relaxed Stabilization Conditions for TS Fuzzy Systems with Optimal Upper Bounds for the Time Derivative of Fuzzy Lyapunov Functions |
title_full |
Relaxed Stabilization Conditions for TS Fuzzy Systems with Optimal Upper Bounds for the Time Derivative of Fuzzy Lyapunov Functions |
title_fullStr |
Relaxed Stabilization Conditions for TS Fuzzy Systems with Optimal Upper Bounds for the Time Derivative of Fuzzy Lyapunov Functions |
title_full_unstemmed |
Relaxed Stabilization Conditions for TS Fuzzy Systems with Optimal Upper Bounds for the Time Derivative of Fuzzy Lyapunov Functions |
title_sort |
Relaxed Stabilization Conditions for TS Fuzzy Systems with Optimal Upper Bounds for the Time Derivative of Fuzzy Lyapunov Functions |
author |
Lazarini, Adalberto Z. N. [UNESP] |
author_facet |
Lazarini, Adalberto Z. N. [UNESP] Teixeira, Marcelo C. M. [UNESP] De S. Ribeiro, Jean M. [UNESP] Assuncao, Edvaldo [UNESP] Cardim, Rodrigo [UNESP] Buzetti, Ariel S. [UNESP] |
author_role |
author |
author2 |
Teixeira, Marcelo C. M. [UNESP] De S. Ribeiro, Jean M. [UNESP] Assuncao, Edvaldo [UNESP] Cardim, Rodrigo [UNESP] Buzetti, Ariel S. [UNESP] |
author2_role |
author author author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Lazarini, Adalberto Z. N. [UNESP] Teixeira, Marcelo C. M. [UNESP] De S. Ribeiro, Jean M. [UNESP] Assuncao, Edvaldo [UNESP] Cardim, Rodrigo [UNESP] Buzetti, Ariel S. [UNESP] |
dc.subject.por.fl_str_mv |
fuzzy control Fuzzy Lyapunov function (FLF) linear matrix inequalities (LMIs) stability stabilization Takagi-Sugeno (TS) fuzzy systems |
topic |
fuzzy control Fuzzy Lyapunov function (FLF) linear matrix inequalities (LMIs) stability stabilization Takagi-Sugeno (TS) fuzzy systems |
description |
This paper initially proposes an optimization problem and after presents its optimal solution. Then, this result is applied to obtain relaxed conditions to design controllers for nonlinear plants described by Takagi-Sugeno (TS) models, based on fuzzy Lyapunov function (FLF) and Linear Matrix Inequalities (LMI). The FLF is given by V(x(t)) = x(t)TP(α (x(t)))x(t), where x(t) is the plant state vector, P(α (x(t))) = α 1(x(t))P1 + α 2(x(t))P2 + c + α r(x(t))Pr, Pi=PiT > 0 and α i(x(t)) is the weight related to the local model i in the representation of the plant by TS fuzzy models, for i=1,2,c,r. When one calculates the time derivative of this V(x(t)), it appears the term x(t)T P(α (x(t)))x(t), that is usually handled using conservative upper bounds, supposing that the bounds of the time derivative of α i(x(t)), i=1,2,c,r, are available. The main result of this paper is a procedure to obtain optimal upper bounds for the term x(t)T P(α (x(t)))x(t), such that they contemplate the maximum value and are always smaller than or equal to the maximum value. It is a relevant result on this subject, because these optimal upper bounds do not add any constraint. With these optimal upper bounds, a relaxed design method for stabilization of TS fuzzy models is proposed. Two numerical examples illustrate the effectiveness of this procedure. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T10:59:04Z 2021-06-25T10:59:04Z 2021-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1109/ACCESS.2021.3076030 IEEE Access, v. 9, p. 64945-64957. 2169-3536 http://hdl.handle.net/11449/207673 10.1109/ACCESS.2021.3076030 2-s2.0-85105044353 |
url |
http://dx.doi.org/10.1109/ACCESS.2021.3076030 http://hdl.handle.net/11449/207673 |
identifier_str_mv |
IEEE Access, v. 9, p. 64945-64957. 2169-3536 10.1109/ACCESS.2021.3076030 2-s2.0-85105044353 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
IEEE Access |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
64945-64957 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808128816408690688 |