A new approach to fuzzy modeling and control of discrete-time systems

Michael Margaliot; Gideon Langholz

doi:10.1109/TFUZZ.2003.814836

A new approach to fuzzy modeling and control of discrete-time systems

Michael Margaliot^*, Gideon Langholz

^*Corresponding author for this work

Engineering General

Research output: Contribution to journal › Article › peer-review

37 Scopus citations

Abstract

We present a new approach to fuzzy modeling and control of discrete-time systems which is based on the formulation of a novel state-space representation using the hyperbolic tangent function. The new representation, designated the hyperbolic model, combines the advantages of fuzzy system theory and classical control theory. On the one hand, the hyperbolic model is easily derived from a set of Mamdani-type fuzzy rules. On the other hand, classical control theory can be applied to design controllers for the hyperbolic model that not only guarantee stability and robustness but are themselves equivalent to a set of Mamdani-type fuzzy rules. Thus, this new approach combines the best of two worlds. It enables linguistic interpretability of both the model and the controller, and guarantees closed-loop stability and robustness.

Original language	English
Pages (from-to)	486-494
Number of pages	9
Journal	IEEE Transactions on Fuzzy Systems
Volume	11
Issue number	4
DOIs	https://doi.org/10.1109/TFUZZ.2003.814836
State	Published - Aug 2003

Keywords

Diagonal stability
Linear matrix inequality
Linguistic interpretability
Nonlinear optimal control
Repeated scalar nonlinearities

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AB - We present a new approach to fuzzy modeling and control of discrete-time systems which is based on the formulation of a novel state-space representation using the hyperbolic tangent function. The new representation, designated the hyperbolic model, combines the advantages of fuzzy system theory and classical control theory. On the one hand, the hyperbolic model is easily derived from a set of Mamdani-type fuzzy rules. On the other hand, classical control theory can be applied to design controllers for the hyperbolic model that not only guarantee stability and robustness but are themselves equivalent to a set of Mamdani-type fuzzy rules. Thus, this new approach combines the best of two worlds. It enables linguistic interpretability of both the model and the controller, and guarantees closed-loop stability and robustness.

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A new approach to fuzzy modeling and control of discrete-time systems

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