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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
Abdalmoaty, M. . & Hjalmarsson, H. (2019). Linear Prediction Error Methods for Stochastic Nonlinear Models. Automatica, 105, 49-63
Open this publication in new window or tab >>Linear Prediction Error Methods for Stochastic Nonlinear Models
2019 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 105, p. 49-63Article in journal (Refereed) Published
Abstract [en]

The estimation problem for stochastic parametric nonlinear dynamical models is recognized to be challenging. The main difficulty is the intractability of the likelihood function and the optimal one-step ahead predictor. In this paper, we present relatively simple prediction error methods based on non-stationary predictors that are linear in the outputs. They can be seen as extensions of the linear identification methods for the case where the hypothesized model is stochastic and nonlinear. The resulting estimators are defined by analytically tractable objective functions in several common cases. It is shown that, under certain identifiability and standard regularity conditions, the estimators are consistent and asymptotically normal. We discuss the relationship between the suggested estimators and those based on second-order equivalent models as well as the maximum likelihood method. The paper is concluded with a numerical simulation example as well as a real-data benchmark problem.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Parameter estimation; System identification; Stochastic systems; Nonlinear models; Prediction error methods.
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-235340 (URN)10.1016/j.automatica.2019.03.006 (DOI)000476963500005 ()2-s2.0-85063614946 (Scopus ID)
Funder
Swedish Research Council, 2015-05285 : 2016-06079
Note

QC 20180921

Available from: 2018-09-21 Created: 2018-09-21 Last updated: 2019-08-12Bibliographically approved
Risuleo, R. S., Bottegal, G. & Hjalmarsson, H. (2019). Modeling and identification of uncertain-input systems. Automatica, 105, 130-141
Open this publication in new window or tab >>Modeling and identification of uncertain-input systems
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
Keywords
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:nbn:se:kth:diva-252499 (URN)10.1016/j.automatica.2019.03.014 (DOI)000476963500013 ()2-s2.0-85063903295 (Scopus ID)
Note

QC 20190711

Available from: 2019-07-11 Created: 2019-07-11 Last updated: 2019-08-12Bibliographically 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: 2019-08-15Bibliographically 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
Valenzuela, P. E., Rojas, C. R. & Hjalmarsson, H. (2018). Analysis of averages over distributions of Markov processes. Automatica, 98, 354-357
Open this publication in new window or tab >>Analysis of averages over distributions of Markov processes
2018 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 98, p. 354-357Article in journal (Refereed) Published
Abstract [en]

In problems of optimal control of Markov decision processes and optimal design of experiments, the occupation measure of a Markov process is designed in order to maximize a specific reward function. When the memory of such a process is too long, or the process is non-Markovian but mixing, it makes sense to approximate it by that of a shorter memory Markov process. This note provides a specific bound for the approximation error introduced in these schemes. The derived bound is then applied to the proposed solution of a recently introduced approach to optimal input design for nonlinear systems.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
System identification, Input design, Markov chains
National Category
Materials Engineering
Identifiers
urn:nbn:se:kth:diva-239469 (URN)10.1016/j.automatica.2018.09.016 (DOI)000449310900039 ()2-s2.0-85053735276 (Scopus ID)
Note

QC 20181126

Available from: 2018-11-26 Created: 2018-11-26 Last updated: 2019-08-20Bibliographically approved
Abdalmoaty, M. . & Hjalmarsson, H. (2018). Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem. In: 18th IFAC Symposium on System Identification: . Paper presented at 18th IFAC Symposium on System Identification, July 9-11, 2018. Stockholm, Sweden.
Open this publication in new window or tab >>Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem
2018 (English)In: 18th IFAC Symposium on System Identification, 2018Conference paper, Published paper (Refereed)
Abstract [en]

The estimation problem of stochastic Wiener-Hammerstein models is recognized to be challenging, mainly due to the analytical intractability of the likelihood function. In this contribution, we apply a computationally attractive prediction error method estimator to a real-data stochastic Wiener-Hammerstein benchmark problem. The estimator is defined using a deterministic predictor that is nonlinear in the input. The prediction error method results in tractable expressions, and Monte Carlo approximations are not necessary. This allows us to tackle several issues considered challenging from the perspective of the current mainstream approach. Under mild conditions, the estimator can be shown to be consistent and asymptotically normal. The results of the method applied to the benchmark data are presentedand discussed.

Series
IFAC-PapersOnLine
Keywords
Nonlinear system identication, Stochastic systems, Wiener-Hammerstein, Benchmark problem.
National Category
Control Engineering Signal Processing
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-233635 (URN)
Conference
18th IFAC Symposium on System Identification, July 9-11, 2018. Stockholm, Sweden
Funder
Swedish Research Council, 2015-05285Swedish Research Council, 2016-06079EU, European Research Council, 267381
Note

QC 20180828

Available from: 2018-08-27 Created: 2018-08-27 Last updated: 2018-08-29Bibliographically approved
Abdalmoaty, M. . & Hjalmarsson, H. (2018). Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem⁎. IFAC-PapersOnLine, 51(15), 784-789
Open this publication in new window or tab >>Application of a Linear PEM Estimator to a Stochastic Wiener-Hammerstein Benchmark Problem⁎
2018 (English)In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 784-789Article in journal (Refereed) Published
Abstract [en]

The estimation problem of stochastic Wiener-Hammerstein models is recognized to be challenging, mainly due to the analytical intractability of the likelihood function. In this contribution, we apply a computationally attractive prediction error method estimator to a real-data stochastic Wiener-Hammerstein benchmark problem. The estimator is defined using a deterministic predictor that is nonlinear in the input. The prediction error method results in tractable expressions, and Monte Carlo approximations are not necessary. This allows us to tackle several issues considered challenging from the perspective of the current mainstream approach. Under mild conditions, the estimator can be shown to be consistent and asymptotically normal. The results of the method applied to the benchmark data are presented and discussed.

Place, publisher, year, edition, pages
Elsevier B.V., 2018
Keywords
Benchmark problem, Nonlinear systems, Stochastic systems, System identification, Wiener-Hammerstein, Error analysis, Identification (control systems), Monte Carlo methods, Stochastic models, Bench-mark problems, Benchmark data, Estimation problem, Likelihood functions, Monte-carlo approximations, Prediction error method, Wiener-hammerstein models, Benchmarking
National Category
Control Engineering
Identifiers
urn:nbn:se:kth:diva-247494 (URN)10.1016/j.ifacol.2018.09.135 (DOI)000446599200133 ()2-s2.0-85054433381 (Scopus ID)
Note

QC 20190403

Available from: 2019-04-03 Created: 2019-04-03 Last updated: 2019-05-20Bibliographically approved
Risuleo, R. S., Bottegal, G. & Hjalmarsson, H. (2018). Approximate Maximum-likelihood Identification of Linear Systems from Quantized Measurements⁎. IFAC-PapersOnLine, 51(15), 724-729
Open this publication in new window or tab >>Approximate Maximum-likelihood Identification of Linear Systems from Quantized Measurements⁎
2018 (English)In: IFAC-PapersOnLine, E-ISSN 2405-8963, Vol. 51, no 15, p. 724-729Article in journal (Refereed) Published
Abstract [en]

We analyze likelihood-based identification of systems that are linear in the parameters from quantized output data; in particular, we propose a method to find approximate maximum-likelihood and maximum-a-posteriori solutions. The method consists of appropriate least-squares projections of the middle point of the active quantization intervals. We show that this approximation maximizes a variational approximation of the likelihood and we provide an upper bound for the approximation error. In a simulation study, we compare the proposed method with the true maximum-likelihood estimate of a finite impulse response model. 

Place, publisher, year, edition, pages
Elsevier B.V., 2018
Keywords
Least-squares approximation, Maximum-likelihood estimators, quantized signals, Impulse response, Least squares approximations, Linear systems, Approximation errors, Finite impulse response model, Identification of systems, Maximum a posteriori solutions, Maximum likelihood estimate, Maximum likelihood estimator, Quantized measurements, Variational approximation, Maximum likelihood estimation
National Category
Signal Processing
Identifiers
urn:nbn:se:kth:diva-247498 (URN)10.1016/j.ifacol.2018.09.169 (DOI)000446599200123 ()2-s2.0-85054371213 (Scopus ID)
Note

QC20190418

Available from: 2019-04-18 Created: 2019-04-18 Last updated: 2019-05-22Bibliographically approved
Abdalmoaty, M. . & Hjalmarsson, H. (2018). Consistent Estimators of Stochastic MIMO Wiener Models based on Suboptimal Predictors. In: : . Paper presented at 57th IEEE Conference on Decision and Control, 17-19 Dec. 2018, Miami Beach, FL, USA. Institute of Electrical and Electronics Engineers (IEEE)
Open this publication in new window or tab >>Consistent Estimators of Stochastic MIMO Wiener Models based on Suboptimal Predictors
2018 (English)Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2018
Keywords
Nonlinear system identification, Multiple-inputs multiple outputs, Wiener Model, Stochastic System, Consistency, Prediction Error Method
National Category
Control Engineering Signal Processing
Research subject
Electrical Engineering
Identifiers
urn:nbn:se:kth:diva-233826 (URN)10.1109/CDC.2018.8618926 (DOI)000458114803091 ()2-s2.0-85062175030 (Scopus ID)
Conference
57th IEEE Conference on Decision and Control, 17-19 Dec. 2018, Miami Beach, FL, USA
Funder
Swedish Research Council, 2015-05285; 2016-06079
Note

QC 20180904

Available from: 2018-08-29 Created: 2018-08-29 Last updated: 2019-04-04Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-9368-3079

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