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System Identification: the State-of-the-Art

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Automating Data-Driven Modelling of Dynamical Systems

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Abstract

Chapter 1 culminated in the formulation of the research objective pursued in this dissertation: to develop a identification methodology that automates the task of system identification form the user’s perspective. The research objective was also dissected into more specific, actionable research questions. The research objective, and the related research question, proposed in Chap. 1 were motivated by the challenges experienced by a user in the typical identification cycle.

An original idea? That can’t be too hard. The library must be full of them.

Steven Fry

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Notes

  1. 1.

    Note that, in the case of linear systems, the errors-in-variables setting reduces to an output-error noise setting, due to the linearity of the system. However, in that case, the noise is correlated with the input, which must be taken into account to accurately estimate a model.

  2. 2.

    Pre- and post-multiplication of \(\hat{\Gamma }_i\) with suitable weighting matrices \(W_1\) and \(W_2\) yield MOESP or CVA algorithms under suitable assumptions. See details in Van Overschee and De Moor [78].

  3. 3.

    As mentioned earlier, while subspace methods can be extended to specific classes of non-linear systems, the extension is usually more involved and require a specially designed numerical methods.

  4. 4.

    A Gaussian Process is a generalization of the Gaussian distribution over functions with a continuous domain, see Rasmussen and Williams [64] for details.

  5. 5.

    These assumptions provide significant computational advantage, as will be discussed in the sequel.

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  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Dhruv Khandelwal

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Khandelwal, D. (2022). System Identification: the State-of-the-Art. In: Automating Data-Driven Modelling of Dynamical Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-90343-5_2

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