Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part II. Control Design

Jafarzadeh, Saeed; Fadali, M. Sami; Sonbol, A.

doi:10.1109/tfuzz.2011.2158219

Cited by 43 publications

(20 citation statements)

References 36 publications

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“…There have been several studies on the stability of IT2 FLCs [2], [7], [18], [19], [23], [24], which include methods for designing stable IT2 FLCs and methods for testing whether an IT2 FLC is stable or not.…”

Section: Stabilitymentioning

confidence: 99%

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Twelve considerations in choosing between Gaussian and trapezoidal membership functions in interval type-2 fuzzy logic controllers

2012

2012 IEEE International Conference on Fuzzy Systems

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Interval type-2 fuzzy logic controllers (IT2 FLCs) have been attracting great research interests recently. There are many decisions to be made in designing an IT2 FLC. One of them is to determine which membership function type to use, e.g., Gaussian or trapezoidal. There have not been comprehensive studies on this problem so far. In this paper we present 12 considerations in choosing between Gaussian and trapezoidal membership functions for an IT2 FLC, including representation, construction, optimization, adaptiveness, novelty, analytical structure, continuity, monotonicity, stability, robustness, computational cost, and control performance. It can help practitioners select the appropriate membership function type in IT2 FLC design, and researchers identify new research opportunities on IT2 FLCs. Our study shows that each MF type has its own advantages: Gaussian IT2 FLCs are simpler in design because they are easier to represent and optimize, always continuous, and faster for small rulebases, whereas trapezoidal IT2 FLCs are simpler in analysis.Index Terms-Interval type-2 fuzzy logic controller, adaptiveness, novelty, analytical structure, continuity, monotonicity, stability, robustness, computational cost U.S. Government work not protected by U.S. copyright WCCI 2012 IEEE World Congress on Computational Intelligence June, 10-15, 2012 -Brisbane, Australia FUZZ IEEE

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Section: Stabilitymentioning

confidence: 99%

“…Jafarzadeh et al [18], [19] proposed sufficient conditions for the exponential stability of T1 and general type-2 TSK FLCs. A major advantage of their approach is that it doe not require the existence of a common Lyapunov function and is therefore applicable to systems with unstable consequents.…”

Section: Stabilitymentioning

confidence: 99%

Twelve considerations in choosing between Gaussian and trapezoidal membership functions in interval type-2 fuzzy logic controllers

2012

2012 IEEE International Conference on Fuzzy Systems

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“…The stability analysis of interval type‐2 (IT2) FMB control systems subject to parameter uncertainties is an interesting research topic to explore. Many studies have focused on applying T2 T‐S fuzzy logic systems in the modeling of uncertain systems, and many successful results have been reported . The authors in Refs investigated the stability analysis of discrete‐time IT2 fuzzy systems.…”

Section: Introductionmentioning

confidence: 99%

Transient stability and voltage regulation in the framework of the interval type‐2 fuzzy model‐based control systems

Abbadi

Hamidia

2019

IEEJ Transactions Elec Engng

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In this paper, the transient stability enhancement and voltage regulation of a multimachine power system are investigated taking into account the generator parameter uncertainties. An interval type‐2 Takagi–Sugeno (IT2 T‐S) fuzzy model is proposed to represent the nonlinear plant subject to parameter uncertainties. New basic concepts of the IT2 T‐S fuzzy model are proposed to reduce considerably the number of models adopted. A Lyapunov‐based approach is employed to analyze the stability and the pole placement of the IT2 fuzzy closed‐loop system formed by the IT‐2 T‐S fuzzy model and the IT‐2 fuzzy controller. This approach presents a simple closed mathematical form that provides the possibility to regulate the system under uncertain model parameters with closed‐loop design specifications as linear matrix inequality (LMI)‐based optimization problems without any assumptions about the membership functions. A simulation example is given to illustrate the effectiveness of the proposed IT‐2 fuzzy model‐based control approach. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

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“…Since then, it has attracted great attention and many fruitful results have been presented in both theory and practice (see, e.g. [9][10][11][12][13][14][15]). One motivation for studying such a class of systems is that type-2 fuzzy sets are better in representing and capturing uncertainties [16,17], especially when the nonlinear plant inevitably suffers the parameter uncertainties while type-1 fuzzy sets do not contain uncertain information.…”

Section: Introductionmentioning

confidence: 99%

Control design for interval type‐2 polynomial fuzzy‐model‐based systems with time‐varying delay

Li¹,

Lam²,

Zhang

2017

IET Control Theory & Applications

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Citing this paper Please note that where the full-text provided on King's Research Portal is the Author Accepted Manuscript or Post-Print version this may differ from the final Published version. If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. And where the final published version is provided on the Research Portal, if citing you are again advised to check the publisher's website for any subsequent corrections. General rightsCopyright and moral rights for the publications made accessible in the Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognize and abide by the legal requirements associated with these rights.•Users may download and print one copy of any publication from the Research Portal for the purpose of private study or research.•You may not further distribute the material or use it for any profit-making activity or commercial gain •You may freely distribute the URL identifying the publication in the Research Portal Take down policy If you believe that this document breaches copyright please contact librarypure@kcl.ac.uk providing details, and we will remove access to the work immediately and investigate your claim. Abstract: In this paper, the problems of stabilization for interval type-2 polynomial fuzzy systems with time-varying delay and parameter uncertainties are investigated. The objective is to design a state-feedback interval type-2 polynomial fuzzy controller such that the closed-loop control system is asymptotically stable. The conditions for the existence of such a controller are delay dependent and membership function dependent in terms of sum-of-squares (SOS). Based on a basic lemma to deal with the delay terms, we formulate and solve the problem with more flexibility due to imperfect premise matching that the number of rules and premise membership functions are not necessary the same between the interval type-2 polynomial fuzzy model and interval type-2 polynomial fuzzy controller. Piecewise linear membership functions approximations enclosing the original lower and upper membership functions are employed to facilitate the stability analysis. A numerical example indicates the effectiveness of the derived results.

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Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part II. Control Design

Cited by 43 publications

References 36 publications

Twelve considerations in choosing between Gaussian and trapezoidal membership functions in interval type-2 fuzzy logic controllers

Twelve considerations in choosing between Gaussian and trapezoidal membership functions in interval type-2 fuzzy logic controllers

Transient stability and voltage regulation in the framework of the interval type‐2 fuzzy model‐based control systems

Control design for interval type‐2 polynomial fuzzy‐model‐based systems with time‐varying delay

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