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Dynamic Local Linear Neuro-Fuzzy Models

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Nonlinear System Identification

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Abstract

This chapter covers dynamic aspects specific to local model networks. The careful interpretation of the local model parameters, which can be understood as local gain and poles, is discussed. It is demonstrated that this interpretation might be dangerous in off-equilibrium regions. Also, the potentially strange effects of interpolating denominator polynomials are analyzed. It can be concluded that extreme care must be taken when models with output feedback are involved with local model architectures. Therefore, the author argues in favor of dynamics representations without output feedback such as NFIR or NOBF. Furthermore, the issue of stability is discussed where local model networks allow for a deeper analysis than alternative architectures. And finally, various more complex approaches known from linear system identification, such as the instrumental variable method or advanced noise models, are transferred to the nonlinear world via local model networks.

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Notes

  1. 1.

    The offsets are not denoted as “c i” in order to avoid confusion with the validity function centers.

  2. 2.

    “Gain scheduling” is the commonly used terminology for parameter scheduling as well. The term “parameter scheduling” is seldom used although it is more exact.

  3. 3.

    The denominator polynomial is assumed to be N(q) = q n + a n−1 q n−1 + … + a 1 q + a 0 (by normalization a n = 1).

  4. 4.

    Approaches that are less sensitive to prior knowledge have been proposed. For example, the Laguerre pole can be estimated by nonlinear optimization, or from an initial NOBF model based on prior knowledge, a better choice for the pole can be found by model reduction techniques (this idea can be applied in an iterative manner). These ideas clearly require further investigation and are not pursued here because they are computationally more demanding than the calculation of a least squares solution.

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    Oliver Nelles

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Nelles, O. (2020). Dynamic Local Linear Neuro-Fuzzy Models. In: Nonlinear System Identification. Springer, Cham. https://doi.org/10.1007/978-3-030-47439-3_22

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