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The transportation distance for fuzzy descriptions of measurements

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Allevard T. , Benoit E. , Foulloy L.

Metrology and Measurement Systems

2007

tom Vol. 14, nr 1

25-37

Fuzzy nominal scales were introduced in order to propose a formalism to the representation of empirical quantities by fuzzy subsets of words. This scale proposes a similarity relation and an associated bounded distance that can be used to perform signal processing on fuzzy subsets of words. Due to the limits of this last distance, we studied distances associated to this formalism and proposed a new distance operator named transportation distance. This paper presents the results of these studies.

Fuzzy feedback linearizing controller and its equivalence with the fuzzy nonlinear internal model control structure

100%

Boukezzoula R. , Galichet S. , Foulloy L.

tom Vol. 17, no 2

233-248

This paper examines the inverse control problem of nonlinear systems with stable dynamics using a fuzzy modeling approach. Indeed, based on the ability of fuzzy systems to approximate any nonlinear mapping, the nonlinear system is represented by a Takagi-Sugeno (TS) fuzzy system, which is then inverted for designing a fuzzy controller. As an application of the proposed inverse control methodology, two popular control structures, namely, feedback linearization and Nonlinear Internal Model Control (NIMC) are investigated. Moreover, the paper points out that, under some conditions, both of the control structures are equivalent and naturally implement a Smith predictor in the presence of time delays.