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Galrinho, Miguel
Publications (9 of 9) Show all publications
Galrinho, M., Rojas, C. R. & Hjalmarsson, H. (2019). Estimating models with high-order noise dynamics using semi-parametric weighted null-space fitting. Automatica, 102, 45-57
Open this publication in new window or tab >>Estimating models with high-order noise dynamics using semi-parametric weighted null-space fitting
2019 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 102, p. 45-57Article in journal (Refereed) Published
Abstract [en]

Standard system identification methods often provide inconsistent estimates with closed-loop data. With the prediction error method (PEM), this issue is solved by using a noise model that is flexible enough to capture the noise spectrum. However, a too flexible noise model (i.e., too many parameters) increases the model complexity, which can cause additional numerical problems for PEM. In this paper, we consider the weighted null-space fitting (WNSF) method. With this method, the system is first modeled using a non-parametric ARX model, which is then reduced to a parametric model of interest using weighted least squares. In the reduction step, a parametric noise model does not need to be estimated if it is not of interest. Because the flexibility of the noise model is increased with the sample size, this will still provide consistent estimates in closed loop and asymptotically efficient estimates in open loop. In this paper, we prove these results, and we derive the asymptotic covariance for the estimation error obtained in closed loop, which is optimal for an infinite-order noise model. For this purpose, we also derive a new technical result for geometric variance analysis, instrumental to our end. Finally, we perform a simulation study to illustrate the benefits of the method when the noise model cannot be parametrized by a low-order model.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Closed-loop identification, Identification algorithms, Least squares, Non-parametric identification, Parameter identification, System identification
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-246463 (URN)10.1016/j.automatica.2018.12.039 (DOI)000461725600006 ()2-s2.0-85060237267 (Scopus ID)
Note

QC 20190326

Available from: 2019-03-26 Created: 2019-03-26 Last updated: 2019-04-09Bibliographically approved
Galrinho, M., Rojas, C. R. & Hjalmarsson, H. (2019). Parametric Identification Using Weighted Null-Space Fitting. IEEE Transactions on Automatic Control, 64(7), 2798-2813
Open this publication in new window or tab >>Parametric Identification Using Weighted Null-Space Fitting
2019 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 64, no 7, p. 2798-2813Article in journal (Refereed) Published
Abstract [en]

In identification of dynamical systems, the prediction error method with a quadratic cost function provides asymptotically efficient estimates under Gaussian noise, but in general it requires solving a nonconvex optimization problem, which may imply convergence to nonglobal minima. An alternative class of methods uses a nonparametric model as intermediate step to obtain the model of interest. Weighted null-space fitting (WNSF) belongs to this class, starting with the estimate of a nonparametric ARX model with least squares. Then, the reduction to a parametric model is a multistep procedure where each step consists of the solution of a quadratic optimization problem, which can be obtained with weighted least squares. The method is suitable for both open- and closed-loop data, and can be applied to many common parametric model structures, including output-error, ARMAX, and Box-Jenkins. The price to pay is the increase of dimensionality in the nonparametric model, which needs to tend to infinity as function of the sample size for certain asymptotic statistical properties to hold. In this paper, we conduct a rigorous analysis of these properties: namely, consistency, and asymptotic efficiency. Also, we perform a simulation study illustrating the performance of WNSF and identify scenarios where it can be particularly advantageous compared with state-of-the-art methods.

Place, publisher, year, edition, pages
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2019
Keywords
Least squares, system identification
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-255416 (URN)10.1109/TAC.2018.2877673 (DOI)000473489700011 ()2-s2.0-85055726363 (Scopus ID)
Note

QC 20190815

Available from: 2019-08-15 Created: 2019-08-15 Last updated: 2019-10-15Bibliographically approved
Weerts, H. H., Galrinho, M., Bottegal, G., Hjalmarsson, H. & den Hof, P. M. (2018). A sequential least squares algorithm for ARMAX dynamic network identification. IFAC-PapersOnLine, 51(15), 844-849
Open this publication in new window or tab >>A sequential least squares algorithm for ARMAX dynamic network identification
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2018 (English)In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 844-849Article in journal (Refereed) Published
Abstract [en]

Identification of dynamic networks in prediction error setting often requires the solution of a non-convex optimization problem, which can be difficult to solve especially for large-scale systems. Focusing on ARMAX models of dynamic networks, we instead employ a method based on a sequence of least-squares steps. For single-input single-output models, we show that the method is equivalent to the recently developed Weighted Null Space Fitting, and, drawing from the analysis of that method, we conjecture that the proposed method is both consistent as well as asymptotically efficient under suitable assumptions. Simulations indicate that the sequential least squares estimates can be of high quality even for short data sets.

Place, publisher, year, edition, pages
Elsevier B.V., 2018
Keywords
dynamic networks, identification algorithm, least squares, System identification, Convex optimization, Identification (control systems), Large scale systems, Asymptotically efficient, Dynamic network, Identification algorithms, Least Square, Least squares algorithm, Least squares estimate, Nonconvex optimization, Single input single output, Least squares approximations
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-247491 (URN)10.1016/j.ifacol.2018.09.119 (DOI)000446599200143 ()2-s2.0-85054462289 (Scopus ID)
Note

QC20190412

Available from: 2019-04-12 Created: 2019-04-12 Last updated: 2019-04-12Bibliographically approved
Ferizbegovic, M., Galrinho, M. & Hjalmarsson, H. (2018). Nonlinear FIR Identification with Model Order Reduction Steiglitz-McBride⁎. IFAC-PapersOnLine, 51(15), 646-651
Open this publication in new window or tab >>Nonlinear FIR Identification with Model Order Reduction Steiglitz-McBride⁎
2018 (English)In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 646-651Article in journal (Refereed) Published
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. 

Place, publisher, year, edition, pages
Elsevier B.V., 2018
Keywords
least-squares identification, non-linear, System identification, Cost functions, Identification (control systems), Impulse response, Model structures, Religious buildings, Asymptotically efficient, Finite impulse response model, Least squares algorithm, Least squares identification, Non linear, Nonconvex cost functions, Prediction error method, Steiglitz-Mcbride method, Least squares approximations
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-247493 (URN)10.1016/j.ifacol.2018.09.218 (DOI)000446599200110 ()2-s2.0-85054449269 (Scopus ID)
Note

QC 20190403

Available from: 2019-04-03 Created: 2019-04-03 Last updated: 2019-05-20Bibliographically approved
Everitt, N., Galrinho, M. & Hjalmarsson, H. (2018). Open-loop asymptotically efficient model reduction with the Steiglitz–McBride method. Automatica, 89, 221-234
Open this publication in new window or tab >>Open-loop asymptotically efficient model reduction with the Steiglitz–McBride method
2018 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 89, p. 221-234Article in journal (Refereed) Published
Abstract [en]

In system identification, it is often difficult to use a physical intuition when choosing a noise model structure. The importance of this choice is that, for the prediction error method (PEM) to provide asymptotically efficient estimates, the model orders must be chosen according to the true system. However, if only the plant estimates are of interest and the experiment is performed in open loop, the noise model can be over-parameterized without affecting the asymptotic properties of the plant. The limitation is that, as PEM suffers in general from non-convexity, estimating an unnecessarily large number of parameters will increase the risk of getting trapped in local minima. Here, we consider the following alternative approach. First, estimate a high-order ARX model with least squares, providing non-parametric estimates of the plant and noise model. Second, reduce the high-order model to obtain a parametric model of the plant only. We review existing methods to do this, pointing out limitations and connections between them. Then, we propose a method that connects favorable properties from the previously reviewed approaches. We show that the proposed method provides asymptotically efficient estimates of the plant with open-loop data. Finally, we perform a simulation study suggesting that the proposed method is competitive with state-of-the-art methods.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
High order arx-modeling, Maximum likelihood, Steiglitz–McBride, System identification
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-220956 (URN)10.1016/j.automatica.2017.12.016 (DOI)000427210200025 ()2-s2.0-85039723128 (Scopus ID)
Funder
Swedish Research Council, 015-05285; 2016-06079
Note

QC 20180110

Available from: 2018-01-10 Created: 2018-01-10 Last updated: 2018-04-05Bibliographically approved
Ferizbegovic, M., Galrinho, M. & Hjalmarsson, H. (2018). Weighted Null-Space Fitting for Cascade Networks with Arbitrary Location of Sensors and Excitation Signals. In: : 2018 IEEE Conference on Decision and Control (CDC): . Paper presented at 57th IEEE Conference on Decision and Control, CDC 2018; Centre of the Fontainebleau in Miami Beach, Miami; United States; 17 December 2018 through 19 December 2018; (pp. 4707-4712). Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>Weighted Null-Space Fitting for Cascade Networks with Arbitrary Location of Sensors and Excitation Signals
2018 (English)In: : 2018 IEEE Conference on Decision and Control (CDC), Institute of Electrical and Electronics Engineers (IEEE), 2018, p. 4707-4712Conference paper, Published 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.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2018
Series
IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-245000 (URN)10.1109/CDC.2018.8619410 (DOI)000458114804056 ()2-s2.0-85062173448 (Scopus ID)978-1-5386-1395-5 (ISBN)
Conference
57th IEEE Conference on Decision and Control, CDC 2018; Centre of the Fontainebleau in Miami Beach, Miami; United States; 17 December 2018 through 19 December 2018;
Note

QC 20190305

Available from: 2019-03-05 Created: 2019-03-05 Last updated: 2019-04-04Bibliographically approved
Galrinho, M., Prota, R., Ferizbegovic, M. & Hjalmarsson, H. (2018). Weighted Null-Space Fitting for Identification of Cascade Networks⁎. IFAC-PapersOnLine, 51(15), 856-861
Open this publication in new window or tab >>Weighted Null-Space Fitting for Identification of Cascade Networks⁎
2018 (English)In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 856-861Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier B.V., 2018
Keywords
least-squares identification, networks, System identification, Cost benefit analysis, Cost functions, Embedded systems, Error analysis, Identification (control systems), Least squares approximations, Networks (circuits), Asymptotic efficiency, Asymptotically efficient, Identification of systems, Least squares identification, Nonconvex cost functions, Prediction error method, Single input single output systems, Weighted least squares, Complex networks
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-247497 (URN)10.1016/j.ifacol.2018.09.116 (DOI)000446599200145 ()2-s2.0-85054379687 (Scopus ID)
Note

QC20190403

Available from: 2019-04-03 Created: 2019-04-03 Last updated: 2019-05-22Bibliographically approved
Galrinho, M., Everitt, N. & Hjalmarsson, H. (2017). Incorporating noise modeling in dynamic networks using non-parametric models. IFAC-PapersOnLine, 50(1), 10568-10573
Open this publication in new window or tab >>Incorporating noise modeling in dynamic networks using non-parametric models
2017 (English)In: IFAC-PapersOnLine, ISSN 2405-8963, Vol. 50, no 1, p. 10568-10573Article in journal (Refereed) Published
Abstract [en]

For identification of systems in dynamic networks, two-stage and instrumental variable methods are common time-domain methods. These methods provide consistent estimates of a chosen module of the network without estimating other parts of the network or noise models. However, disregarding noise modeling may come at a cost in estimation error. To capture the noise contribution, we propose the following procedure: first, we estimate a non-parametric model of an appropriate part of the network; second, we estimate the module of interest using signals simulated with the non-parametric model. The simulated signals are derived from an asymptotic maximum likelihood criterion. Preliminary simulations suggest that the propose method is competitive with existing approaches and is particularly beneficial with colored noise.

Place, publisher, year, edition, pages
Elsevier, 2017
Keywords
least-squares identification, networks, System identification
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-223070 (URN)10.1016/j.ifacol.2017.08.1302 (DOI)000423965100254 ()2-s2.0-85031794790 (Scopus ID)
Funder
Swedish Research Council, 2015-05285, 2016-06079
Note

QC 20180213

Available from: 2018-02-13 Created: 2018-02-13 Last updated: 2018-03-05Bibliographically approved
Fang, M., Galrinho, M. & Hjalmarsson, H. (2017). Recursive Identification Based on Weighted Null-Space Fitting. In: 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC): . Paper presented at IEEE 56th Annual Conference on Decision and Control (CDC), DEC 12-15, 2017, Melbourne, AUSTRALIA. IEEE
Open this publication in new window or tab >>Recursive Identification Based on Weighted Null-Space Fitting
2017 (English)In: 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC), IEEE , 2017Conference paper, Published paper (Refereed)
Abstract [en]

Algorithms for online system identification consist in updating the estimated model while data are being collected. A standard method for online identification of structured models is the recursive prediction error method (PEM). The problem is that PEM does not have an exact recursive formulation, and the need to rely on approximations makes recursive PEM prone to convergence problems. In this paper, we propose a recursive implementation of weighted null-space fitting, an asymptotically efficient method for identification of structured models. Consisting only of (weighted) least-squares steps, the recursive version of the algorithm has the same convergence and statistical properties of the off-line version. We illustrate these properties with a simulation study, where the proposed algorithm always attains the performance of the off-line version, while recursive PEM often fails to converge.

Place, publisher, year, edition, pages
IEEE, 2017
Series
IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
urn:nbn:se:kth:diva-223849 (URN)10.1109/CDC.2017.8264345 (DOI)000424696904077 ()2-s2.0-85046134044 (Scopus ID)978-1-5090-2873-3 (ISBN)
Conference
IEEE 56th Annual Conference on Decision and Control (CDC), DEC 12-15, 2017, Melbourne, AUSTRALIA
Funder
Swedish Research Council
Note

QC 20180306

Available from: 2018-03-06 Created: 2018-03-06 Last updated: 2018-11-19Bibliographically approved
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