Modeling and identification of uncertain-input systems

Riccardo Sven Risuleo (Corresponding author), Giulio Bottegal, Håkan Hjalmarsson

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about the input or the linear system, we use Gaussian-process models. We estimate the model from data using the empirical Bayes approach: the hyperparameters that characterize the Gaussian-process models are estimated from the marginal likelihood of the data. We propose an iterative algorithm to find the hyperparameters that relies on the EM method and results in decoupled update steps. Because in the uncertain-input setting neither the marginal likelihood nor the posterior distribution of the unknowns is tractable, we develop an approximation approach based on variational Bayes. As part of the contribution of the paper, we show that this model structure encompasses many classical problems in system identification such as Hammerstein models, blind system identification, and cascaded linear systems. This connection allows us to build a systematic procedure that applies effectively to all the aforementioned problems, as shown in the numerical simulations presented in the paper.

LanguageEnglish
Pages130-141
Number of pages12
JournalAutomatica
Volume105
DOIs
StatePublished - 1 Jul 2019

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Linear systems
Identification (control systems)
Model structures
Computer simulation

Keywords

  • Estimation algorithms
  • Gaussian processes
  • Nonlinear models
  • Nonparametric identification
  • System identification

Cite this

Risuleo, R. S., Bottegal, G., & Hjalmarsson, H. (2019). Modeling and identification of uncertain-input systems. Automatica, 105, 130-141. DOI: 10.1016/j.automatica.2019.03.014
Risuleo, Riccardo Sven ; Bottegal, Giulio ; Hjalmarsson, Håkan. / Modeling and identification of uncertain-input systems. In: Automatica. 2019 ; Vol. 105. pp. 130-141
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Risuleo, RS, Bottegal, G & Hjalmarsson, H 2019, 'Modeling and identification of uncertain-input systems' Automatica, vol. 105, pp. 130-141. DOI: 10.1016/j.automatica.2019.03.014

Modeling and identification of uncertain-input systems. / Risuleo, Riccardo Sven (Corresponding author); Bottegal, Giulio; Hjalmarsson, Håkan.

In: Automatica, Vol. 105, 01.07.2019, p. 130-141.

Research output: Contribution to journalArticleAcademicpeer-review

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Risuleo RS, Bottegal G, Hjalmarsson H. Modeling and identification of uncertain-input systems. Automatica. 2019 Jul 1;105:130-141. Available from, DOI: 10.1016/j.automatica.2019.03.014