Kernel-based methods for Volterra series identification

doi:10.1016/j.automatica.2021.109686

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Kernel-based methods for Volterra series identification

2021-07-01

Alberto Dalla Libera *

Ruggero Carli

Gianluigi Pillonetto

DOI：10.1016/j.automatica.2021.109686

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Abstract

En 中文

Volterra series approximate a broad range of nonlinear systems. Their identification is challenging due to the curse of dimensionality: the number of model parameters grows exponentially with the complexity of the input-output response. This fact limits the applicability of such models and has stimulated recently much research on regularized solutions. Along this line, we propose two new strategies that use kernel-based methods. First, we introduce the multiplicative polynomial kernel (MPK). Compared to the standard polynomial kernel, the MPK is equipped with a richer set of hyperparameters, increasing flexibility in selecting the monomials that really influence the system output. Second, we introduce the smooth exponentially decaying multiplicative polynomial kernel (SEDMPK), that is a regularized version of MPK which requires less hyperparameters, allowing to handle also high-order Volterra series. Numerical results show the effectiveness of the two approaches. (C) 2021 Elsevier Ltd. All rights reserved.

Keywords:

Nonlinear system identification

Nonparametric methods

Time series modeling

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