Efficient identification of linear, parameter-varying, and nonlinear systems with noise models

Fuente: arXiv
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Main Authors: Bemporad, Alberto, Tóth, Roland
Format: Preprint
Published: 2025
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author Bemporad, Alberto
Tóth, Roland
author_facet Bemporad, Alberto
Tóth, Roland
contents We present a general system identification procedure capable of estimating of a broad spectrum of state-space dynamical models, including linear time-invariant (LTI), linear parameter-varying} (LPV), and nonlinear (NL) dynamics, along with rather general classes of noise models. Similar to the LTI case, we show that for this general class of model structures, including the NL case, the model dynamics can be separated into a deterministic process and a stochastic noise part, allowing to seamlessly tune the complexity of the combined model both in terms of nonlinearity and noise modeling. We parameterize the involved nonlinear functional relations by means of artificial neural-networks (ANNs), although alternative parametric nonlinear mappings can also be used. To estimate the resulting model structures, we optimize a prediction-error-based criterion using an efficient combination of a constrained quasi-Newton approach and automatic differentiation, achieving training times in the order of seconds compared to existing state-of-the-art ANN methods which may require hours for models of similar complexity. We formally establish the consistency guarantees for the proposed approach and demonstrate its superior estimation accuracy and computational efficiency on several benchmark LTI, LPV, and NL system identification problems.
format Preprint
id arxiv_https___arxiv_org_abs_2504_11982
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Efficient identification of linear, parameter-varying, and nonlinear systems with noise models
Bemporad, Alberto
Tóth, Roland
Optimization and Control
Machine Learning
Systems and Control
We present a general system identification procedure capable of estimating of a broad spectrum of state-space dynamical models, including linear time-invariant (LTI), linear parameter-varying} (LPV), and nonlinear (NL) dynamics, along with rather general classes of noise models. Similar to the LTI case, we show that for this general class of model structures, including the NL case, the model dynamics can be separated into a deterministic process and a stochastic noise part, allowing to seamlessly tune the complexity of the combined model both in terms of nonlinearity and noise modeling. We parameterize the involved nonlinear functional relations by means of artificial neural-networks (ANNs), although alternative parametric nonlinear mappings can also be used. To estimate the resulting model structures, we optimize a prediction-error-based criterion using an efficient combination of a constrained quasi-Newton approach and automatic differentiation, achieving training times in the order of seconds compared to existing state-of-the-art ANN methods which may require hours for models of similar complexity. We formally establish the consistency guarantees for the proposed approach and demonstrate its superior estimation accuracy and computational efficiency on several benchmark LTI, LPV, and NL system identification problems.
title Efficient identification of linear, parameter-varying, and nonlinear systems with noise models
topic Optimization and Control
Machine Learning
Systems and Control
url https://arxiv.org/abs/2504.11982