Observer Design and H∞ Performance for Discrete-Time Uncertain Fuzzy-Logic Systems

The observer design and <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> algorithm are proposed for the discrete-time fuzzy-logic systems in this article. The considered fuzzy-logic systems are subject to parameter uncertainty and...

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Bibliographic Details
Published in:IEEE transactions on cybernetics Vol. 51; no. 5; pp. 2398 - 2408
Main Authors: Wu, Ailong, Liu, Huan, Zeng, Zhigang
Format: Journal Article
Language:English
Published: United States IEEE 01.05.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H ∞ performance
Algorithms
Discrete time systems
Fuzzy logic
Fuzzy sets
Fuzzy systems
Fuzzy-logic systems
H infinity
Indexes
Nonlinear systems
Observers
Parameter uncertainty
Situational awareness
state estimation
State variable
Uncertain systems
Uncertainty
unmeasurable state variables
ISSN:2168-2267, 2168-2275, 2168-2275
Online Access:Get full text
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Summary:The observer design and <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> algorithm are proposed for the discrete-time fuzzy-logic systems in this article. The considered fuzzy-logic systems are subject to parameter uncertainty and unmeasurable state variables. To appropriately deal with parameter uncertainty and unmeasurable state variables, we first disintegrate the space of premise variables, then the total partitioned regions will be divided into two kinds: 1) crisp regions and 2) fuzzy regions. With the aid of partitioned regions, piecewise fuzzy <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> observers are presented. Availability of the piecewise fuzzy <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> observers gives us an accurate picture of the overall evolution of the augmented systems leading therefore to an improved situational awareness for the noncoordination of premise variables and external interference and, hence, the augmented systems achieve the performance conditions: asymptotic convergence and <inline-formula> <tex-math notation="LaTeX">H_{\infty } </tex-math></inline-formula> performance. The simulation results of the proposed approach show the accuracy of the resulting state estimates.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2019.2948562