Avoiding the matrix inversion in Takagi-Sugeno-based advanced controllers and observers

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dc.creatorThomas Laurain
dc.creatorJimmy Lauber
dc.creatorReinaldo Martinez Palhares
dc.date.accessioned2025-04-22T14:46:13Z
dc.date.accessioned2025-09-09T01:08:36Z
dc.date.available2025-04-22T14:46:13Z
dc.date.issued2018
dc.identifier.doihttps://doi.org/10.1109/TFUZZ.2017.2647992
dc.identifier.issn1063-6706
dc.identifier.urihttps://hdl.handle.net/1843/81736
dc.languageeng
dc.publisherUniversidade Federal de Minas Gerais
dc.relation.ispartofIEEE Transactions on fuzzy systems
dc.rightsAcesso Restrito
dc.subjectSistemas difusos
dc.subjectSistemas não lineares
dc.subjectControle de Processos
dc.subjectInteligência Computacional
dc.subject.otherDiscrete time
dc.subject.otherMatrix inversion approximation
dc.subject.otherMultiple sums fuzzy matrices
dc.subject.otherNonlinear control and estimation
dc.subject.otherObserver-based controller
dc.subject.otherTakagi–Sugeno (TS) representation
dc.titleAvoiding the matrix inversion in Takagi-Sugeno-based advanced controllers and observers
dc.typeArtigo de periódico
local.citation.epage225
local.citation.issue1
local.citation.spage216
local.citation.volume26
local.description.resumoMany of the recent advances on control and estimation of systems described by Takagi-Sugeno (TS) fuzzy models are based on matrix inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this matrix inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the matrix inversion by multiple sums and the second methodology is based on an estimation of the matrix inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.
local.publisher.countryBrasil
local.publisher.departmentENG - DEPARTAMENTO DE ENGENHARIA ELETRÔNICA
local.publisher.initialsUFMG
local.url.externahttps://ieeexplore.ieee.org/document/7807204

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