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  • 1.
    Ferizbegovic, Mina
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Galrinho, Miguel
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
    Nonlinear FIR Identification with Model Order Reduction Steiglitz-McBride⁎2018In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 646-651Article in journal (Refereed)
    Abstract [en]

    In system identification, many structures and approaches have been proposed to deal with systems with non-linear behavior. When applicable, the prediction error method, analogously to the linear case, requires minimizing a cost function that is non-convex in general. The issue with non-convexity is more problematic for non-linear models, not only due to the increased complexity of the model, but also because methods to provide consistent initialization points may not be available for many model structures. In this paper, we consider a non-linear rational finite impulse response model. We observe how the prediction error method requires minimizing a non-convex cost function, and propose a three-step least-squares algorithm as an alternative procedure. This procedure is an extension of the Model Order Reduction Steiglitz-McBride method, which is asymptotically efficient in open loop for linear models. We perform a simulation study to illustrate the applicability and performance of the method, which suggests that it is asymptotically efficient. 

  • 2.
    Ferizbegovic, Mina
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Galrinho, Miguel
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.
    Weighted Null-Space Fitting for Cascade Networks with Arbitrary Location of Sensors and Excitation Signals2018In: : 2018 IEEE Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 4707-4712Conference paper (Refereed)
    Abstract [en]

    Identification of a complete dynamic network affected by sensor noise using the prediction error method is often too complex. One of the reasons for this complexity is the requirement to minimize a non-convex cost function, which becomes more difficult with more complex networks. In this paper, we consider serial cascade networks affected by sensor noise. Recently, the Weighted Null-Space Fitting method has been shown to be appropriate for this setting, providing asymptotically efficient estimates without suffering from non-convexity; however, applicability of the method was subject to some conditions on the locations of sensors and excitation signals. In this paper, we drop such conditions, proposing an extension of the method that is applicable to general serial cascade networks. We formulate an algorithm that describes application of the method in a general setting, and perform a simulation study to illustrate the performance of the method, which suggests that this extension is still asymptotically efficient.

  • 3.
    Galrinho, Miguel
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Prota, R.
    Ferizbegovic, Mina
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Hjalmarsson, Håkan
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Weighted Null-Space Fitting for Identification of Cascade Networks⁎2018In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 856-861Article in journal (Refereed)
    Abstract [en]

    For identification of systems embedded in dynamic networks, the prediction error method (PEM) with a correct parametrization of the complete network provides asymptotically efficient estimates. However, the network complexity often hinders a successful application of PEM, which requires minimizing a non-convex cost function that can become more intricate for more complex networks. For this reason, identification in dynamic networks often focuses in obtaining consistent estimates of modules of interest. A downside of these approaches is that splitting the network in several modules for identification often costs asymptotic efficiency. In this paper, we consider dynamic networks with the modules connected in serial cascade, with measurements affected by sensor noise. We propose an algorithm that estimates all the modules in the network simultaneously without requiring the minimization of a non-convex cost function. This algorithm is an extension of Weighted Null-Space Fitting (WNSF), a weighted least-squares method that provides asymptotically efficient estimates for single-input single-output systems. We illustrate the performance of the algorithm with simulation studies, which suggest that a network WNSF method may also be asymptotically efficient when applied to cascade structures. Finally, we discuss the possibility of extension to more general networks affected by sensor noise.

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