Hankel-Norm-Based Model Reduction for Stochastic Discrete-Time Nonlinear Systems in Interval Type-2 T-S Fuzzy Framework

This article is concerned with the problem of the Hankel-norm model reduction for stochastic discrete-time nonlinear systems in interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy framework. The IT2 T-S fuzzy model is an efficient model for describing uncertain nonlinear systems, and the model reduction...

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Veröffentlicht in:IEEE transactions on cybernetics Jg. 51; H. 10; S. 4934 - 4943
Hauptverfasser: Zeng, Yi, Lam, Hak-Keung, Wu, Ligang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.10.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Analytical models
Complex systems
Discrete time systems
Fuzzy systems
Hankel-norm-based model reduction
interval type-2 Takagi–Sugeno (IT2 T–S) fuzzy model
Linear matrix inequalities
Mathematical analysis
Mathematical model
membership-functions-dependent (MFD) technique
Model reduction
Nonlinear systems
Reduced order systems
stochastic nonlinear systems
Stochastic processes
Symmetric matrices
ISSN:2168-2267, 2168-2275, 2168-2275
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Zusammenfassung:This article is concerned with the problem of the Hankel-norm model reduction for stochastic discrete-time nonlinear systems in interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy framework. The IT2 T-S fuzzy model is an efficient model for describing uncertain nonlinear systems, and the model reduction is to simplify the high-order complex systems by reducing the order of the original system. The aim of this article is to reduce the order of the original stochastic discrete-time IT2 fuzzy system into lower order system without ignoring the influence of IT2 membership functions. First, the Hankel-norm performance of the stochastic discrete-time IT2 fuzzy model is analyzed. Then, based on the projection theorem and cone complementary linearization approach, a convex Hankel-norm-based model reduction approach subject to conditions in the form of linear matrix inequalities (LMIs) is obtained. A membership-functions-dependent (MFD) technique is applied to capture the information of IT2 membership functions and further reduce the conservativeness. A numerical example is presented to illustrate the effectiveness of the proposed results.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2019.2950565