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Modeling and identification of uncertain-input systems
KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-2831-2909
Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0002-9368-3079
2019 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 105, p. 130-141Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 105, p. 130-141
Keywords [en]
Estimation algorithms, Gaussian processes, Nonlinear models, Nonparametric identification, System identification, Gaussian noise (electronic), Identification (control systems), Iterative methods, Linear systems, Religious buildings, Blind system identification, Empirical Bayes approach, Estimation algorithm, Non-linear model, Non-parametric identification, Posterior distributions, System identification problems, Gaussian distribution
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-252499DOI: 10.1016/j.automatica.2019.03.014ISI: 000476963500013Scopus ID: 2-s2.0-85063903295OAI: oai:DiVA.org:kth-252499DiVA, id: diva2:1336969
Note

QC 20190711

Available from: 2019-07-11 Created: 2019-07-11 Last updated: 2019-08-12Bibliographically approved

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Risuleo, Riccardo SvenBottegal, GiulioHjalmarsson, Håkan

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