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Lyzell, Christian
Publications (10 of 18) Show all publications
Schoukens, M., Lyzell, C. & Enqvist, M. (2013). Combining the best linear approximation and dimension reduction to identify the linear blocks of parallel Wiener systems. In: Proceedings of the 11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing: . Paper presented at 11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, Caen, France, July 3-5, 2013 (pp. 372-377).
Open this publication in new window or tab >>Combining the best linear approximation and dimension reduction to identify the linear blocks of parallel Wiener systems
2013 (English)In: Proceedings of the 11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, 2013, p. 372-377Conference paper, Published paper (Refereed)
Abstract [en]

A Wiener model is a fairly simple, well known, and often used nonlinear block- oriented black-box model. A possible generalization of the class of Wiener models lies in the parallel Wiener model class. This paper presents a method to estimate the linear time-invariant blocks of such parallel Wiener models from input/output data only. The proposed estimation method combines the knowledge obtained by estimating the best linear approximation of a nonlinear system with the MAVE dimension reduction method to estimate the linear time- invariant blocks present in the model. The estimation of the static nonlinearity boils down to a standard static nonlinearity estimation problem starting from input-output data once the linear blocks are known. 

Series
IFAC-PapersOnLine, ISSN 2405-8963 ; 46(11)
Keywords
Nonlinear system identification, Nonlinear systems
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-104001 (URN)10.3182/20130703-3-FR-4038.00026 (DOI)
Conference
11th IFAC International Workshop on Adaptation and Learning in Control and Signal Processing, Caen, France, July 3-5, 2013
Available from: 2014-02-05 Created: 2014-02-05 Last updated: 2016-06-22
Lyzell, C., Andersen, M. & Enqvist, M. (2012). A Convex Relaxation of a Dimension Reduction Problem Using the Nuclear Norm. In: Proceedings of the 51st IEEE Conference on Decision and Control: . Paper presented at 51st IEEE Conference on Decision and Control, Maui, Hawaii, USA, 10-13 December, 2012 (pp. 2852-2857).
Open this publication in new window or tab >>A Convex Relaxation of a Dimension Reduction Problem Using the Nuclear Norm
2012 (English)In: Proceedings of the 51st IEEE Conference on Decision and Control, 2012, p. 2852-2857Conference paper, Published paper (Refereed)
Abstract [en]

The estimation of nonlinear models can be a challenging problem, in particular when the number of available data points is small or when the dimension of the regressor space is high. To meet these challenges, several dimension reduction methods have been proposed in the literature, where a majority of the methods are based on the framework of inverse regression. This allows for the use of standard tools when analyzing the statistical properties of an approach and often enables computationally efficient implementations. The main limitation of the inverse regression approach to dimension reduction is the dependence on a design criterion which restricts the possible distributions of the regressors. This limitation can be avoided by using a forward approach, which will be the topic of this paper. One drawback with the forward approach to dimension reduction is the need to solve nonconvex optimization problems. In this paper, a reformulation of a well established dimension reduction method is presented, which reveals the structure of the optimization problem, and a convex relaxation is derived.

Keywords
Concave programming, Nonlinear estimation, Regression analysis
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-93281 (URN)10.1109/CDC.2012.6426097 (DOI)000327200403035 ()978-1-4673-2064-1 (ISBN)978-1-4673-2065-8 (ISBN)
Conference
51st IEEE Conference on Decision and Control, Maui, Hawaii, USA, 10-13 December, 2012
Available from: 2013-05-29 Created: 2013-05-29 Last updated: 2016-06-22
Schoukens, M., Lyzell, C. & Enqvist, M. (2012). Combining the best linear approximation and dimension reduction to identify thelinear blocks of parallel Wiener systems. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Combining the best linear approximation and dimension reduction to identify thelinear blocks of parallel Wiener systems
2012 (English)Report (Other academic)
Abstract [en]

A Wiener model is a fairly simple, well known, and often used nonlinearblock-oriented black-box model. A possible generalization of the class ofWiener models lies in the parallel Wiener model class. This paper presents amethod to estimate the linear time-invariant blocks of such parallel Wienermodels from input/output data only. The proposed estimation methodcombines the knowledge obtained by estimating the best linear approxima-tion of a nonlinear system with a dimension reduction method to estimatethe linear time-invariant blocks present in the model. The estimation of thestatic nonlinearity is fairly easy once the linear blocks are known.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. p. 15
Series
LiTH-ISY-R, ISSN 1400-3902 ; 3050
Keywords
System identification, Wiener systems, Best linear approximation, Dimension reduction
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-84517 (URN)LiTH-ISY-R-3050 (ISRN)
Available from: 2012-10-11 Created: 2012-10-11 Last updated: 2014-09-19Bibliographically approved
Lyzell, C. & Enqvist, M. (2012). Inverse Regression for the Wiener Class of Systems. In: Proceedings of the 16th IFAC Symposium on System Identification: . Paper presented at 16th IFAC Symposium on System Identification, Brussels, Belgium, 11-13 July, 2012 (pp. 476-481).
Open this publication in new window or tab >>Inverse Regression for the Wiener Class of Systems
2012 (English)In: Proceedings of the 16th IFAC Symposium on System Identification, 2012, p. 476-481Conference paper, Published paper (Refereed)
Abstract [en]

The concept of inverse regression has turned out to be quite useful for dimension reduction in regression analysis problems. Using methods like sliced inverse regression (SIR) and directional regression (DR), some high-dimensional nonlinear regression problems can be turned into more tractable low-dimensional problems. Here, the usefulness of inverse regression for identification of nonlinear dynamical systems will be discussed. In particular, it will be shown that the inverse regression methods can be used for identification of systems of the Wiener class, that is, systems consisting of a number of parallel linear subsystems followed by a static multiple-input single-output nonlinearity. For a particular class of input signals, including Gaussian signals, the inverse regression approach makes it possible to estimate the linear subsystems without knowing or estimating the nonlinearity.

Series
IFAC-PapersOnLine, ISSN 2405-8963 ; 45(16)
Keywords
Nonlinear system identification, Nonparametric methods
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-93280 (URN)10.3182/20120711-3-BE-2027.00286 (DOI)978-3-902823-06-9 (ISBN)
Conference
16th IFAC Symposium on System Identification, Brussels, Belgium, 11-13 July, 2012
Available from: 2013-05-29 Created: 2013-05-29 Last updated: 2016-06-22
Lyzell, C. & Enqvist, M. (2012). Sliced Inverse Regression for the Identification of Dynamical Systems. In: Proceedings of the 16th IFAC Symposium on System Identification: . Paper presented at 16th IFAC Symposium on System Identification, Brussels, Belgium, July 11-13, 2012 (pp. 1575-1580).
Open this publication in new window or tab >>Sliced Inverse Regression for the Identification of Dynamical Systems
2012 (English)In: Proceedings of the 16th IFAC Symposium on System Identification, 2012, p. 1575-1580Conference paper, Published paper (Refereed)
Abstract [en]

The estimation of nonlinear functions can be challenging when the number of independent variables is high. This difficulty may, in certain cases, be reduced by first projecting the independent variables on a lower dimensional subspace before estimating the nonlinearity. In this paper, a statistical nonparametric dimension reduction method called sliced inverse regression is presented and a consistency analysis for dynamically dependent variables is given. The straightforward system identification application is the estimation of the number of linear subsystems in a Wiener class system and their corresponding impulse response.

Series
IFAC-PapersOnLine, ISSN 2405-8963 ; 45(16)
Keywords
Nonlinear System Identification, Nonparametric Methods
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-93279 (URN)10.3182/20120711-3-BE-2027.00271 (DOI)
Conference
16th IFAC Symposium on System Identification, Brussels, Belgium, July 11-13, 2012
Available from: 2013-05-29 Created: 2013-05-29 Last updated: 2016-06-22
Lyzell, C. (2012). Structural Reformulations in System Identification. (Doctoral dissertation). Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Structural Reformulations in System Identification
2012 (English)Doctoral thesis, monograph (Other academic)
Abstract [en]

In system identification, the choice of model structure is important and it is sometimes desirable to use a flexible model structure that is able to approximate a wide range of systems. One such model structure is the Wiener class of systems, that is, systems where the input enters a linear time-invariant subsystem followed by a time-invariant nonlinearity. Given a sequence of input and output pairs, the system identification problem is often formulated as the minimization of the mean-square prediction error. Here, the prediction error has a nonlinear dependence on the parameters of the linear subsystem and the nonlinearity. Unfortunately, this formulation of the estimation problem is often nonconvex, with several local minima, and it is therefore difficult to guarantee that a local search algorithm will be able to find the global optimum.

In the first part of this thesis, we consider the application of dimension reduction methods to the problem of estimating the impulse response of the linear part of a system in the Wiener class. For example, by applying the inverse regression approach to dimension reduction, the impulse response estimation problem can be cast as a principal components problem, where the reformulation is based on simple nonparametric estimates of certain conditional moments. The inverse regression approach can be shown to be consistent under restrictions on the distribution of the input signal provided that the true linear subsystem has a finite impulse response. Furthermore, a forward approach to dimension reduction is also considered, where the time-invariant nonlinearity is approximated by a local linear model. In this setting, the impulse response estimation problem can be posed as a rank-reduced linear least-squares problem and a convex relaxation can be derived.

Thereafter, we consider the extension of the subspace identification approach to include linear time-invariant rational models. It turns out that only minor structural modifications are needed and already available implementations can be used. Furthermore, other a priori information regarding the structure of the system can incorporated, including a certain class of linear gray-box structures. The proposed extension is not restricted to the discrete-time case and can be used to estimate continuous-time models.

The final topic in this thesis is the estimation of discrete-time models containing polynomial nonlinearities. In the continuous-time case, a constructive algorithm based on differential algebra has previously been used to prove that such model structures are globally identifiable if and only if they can be written as a linear regression model. Thus, if we are able to transform the nonlinear model structure into a linear regression model, the parameter estimation problem can be solved with standard methods. Motivated by the above and the fact that most system identification problems involve sampled data, a discrete-time version of the algorithm is developed. This algorithm is closely related to the continuous-time version and enables the handling of noise signals without differentiations.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. p. 163
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1475
Keywords
System identification, Dimension reduction, Subspace identification, Difference algebra
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-84515 (URN)978-91-7519-800-2 (ISBN)
Public defence
2012-11-22, Visionen, Hus B, Campus Valla, Linköping universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Funder
Swedish Research Council
Available from: 2012-10-22 Created: 2012-10-10 Last updated: 2019-12-10Bibliographically approved
Lyzell, C., Glad, T., Enqvist, M. & Ljung, L. (2011). Difference Algebra and System Identification. Automatica, 47(9), 1896-1904
Open this publication in new window or tab >>Difference Algebra and System Identification
2011 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 47, no 9, p. 1896-1904Article in journal (Refereed) Published
Abstract [en]

The framework of differential algebra, especially Ritts algorithm, has turned out to be a useful tool when analyzing the identifiability of certain nonlinear continuous-time model structures. This framework provides conceptually interesting means to analyze complex nonlinear model structures via the much simpler linear regression models. One difficulty when working with continuous-time signals is dealing with white noise in nonlinear systems. In this paper, difference algebraic techniques, which mimic the differential-algebraic techniques, are presented. Besides making it possible to analyze discrete-time model structures, this opens up the possibility of dealing with noise. Unfortunately, the corresponding discrete-time identifiability results are not as conclusive as in continuous time. In addition, an alternative elimination scheme to Ritts algorithm will be formalized and the resulting algorithm is analyzed when applied to a special form of the NFIR model structure.

Place, publisher, year, edition, pages
Elsevier, 2011
Keywords
System identification, Identifiability, Ritts algorithm
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-71084 (URN)10.1016/j.automatica.2011.06.013 (DOI)000294877400006 ()
Projects
CADICS
Funder
Swedish Research CouncilVinnova
Available from: 2011-09-30 Created: 2011-09-30 Last updated: 2017-12-08
Lyzell, C. & Enqvist, M. (2011). Inverse Regression for the Wiener Class of Systems. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Inverse Regression for the Wiener Class of Systems
2011 (English)Report (Other academic)
Abstract [en]

The concept of inverse regression has turned out to be quite useful for dimension reduction in regression analysis problems. Using methods like sliced inverse regression (SIR) and directional regression (DR), some high-dimensional nonlinear regression problems can be turned into more tractable low-dimensional problems. Here, the usefulness of inverse regression for identification of nonlinear dynamical systems will be discussed. In particular, it will be shown that the inverse regression methods can be used for identification of systems of the Wiener class, that is, systems consisting of a number of parallel linear subsystems followed by a static multiple-input single-output nonlinearity. For a particular class of input signals, including Gaussian signals, the inverse regression approach makes it possible to estimate the linear subsystems without knowing or estimating the nonlinearity.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2011. p. 14
Series
LiTH-ISY-R, ISSN 1400-3902 ; 3032
Keywords
Nonlinear system identification, Nonparametric methods
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-97974 (URN)LiTH-ISY-R-3032 (ISRN)
Available from: 2013-09-23 Created: 2013-09-23 Last updated: 2014-09-01Bibliographically approved
Lyzell, C. & Enqvist, M. (2011). Sliced Inverse Regression for the Identification of Dynamical Systems. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Sliced Inverse Regression for the Identification of Dynamical Systems
2011 (English)Report (Other academic)
Abstract [en]

The estimation of nonlinear functions can be challenging when the number of independent variables is high. This difficulty may, in certain cases, be reduced by first projecting the independent variables on a lower dimensional subspace before estimating the nonlinearity. In this paper, a statistical nonparametric dimension reduction method called sliced inverse regression is presented and a consistency analysis for dynamically dependent variables is given. The straightforward system identification application is the estimation of the number of linear subsystems in a Wiener class system and their corresponding impulse response.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2011. p. 16
Series
LiTH-ISY-R, ISSN 1400-3902 ; 3031
Keywords
Nonlinear System Identification, Nonparametric Methods
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-97973 (URN)LiTH-ISY-R-3031 (ISRN)
Available from: 2013-09-23 Created: 2013-09-23 Last updated: 2014-09-01Bibliographically approved
Toth, R., Lyzell, C., Enqvist, M., Heuberger, P. S. .. & Van den Hof, P. M. J. (2010). Order and Structural Dependence Selection of LPV-ARX Models using a Nonnegative Garrote Approach. Linköping: Linköping University Electronic Press
Open this publication in new window or tab >>Order and Structural Dependence Selection of LPV-ARX Models using a Nonnegative Garrote Approach
Show others...
2010 (English)Report (Other academic)
Abstract [en]

In order to accurately identify Linear Parameter-Varying (LPV) systems, order selection of LPV linear regression models has prime importance. Existing identification approaches in this context suffer from the drawback that a set of functional dependencies needs to be chosen a priori for the parametrization of the model coefficients. However in a black-box setting, it has not been possible so far to decide which functions from a given set are required for the parametrization and which are not. To provide a practical solution, a nonnegative garrote approach is applied. It is shown that using only a measured data record of the plant, both the order selection and the selection of structural coefficient dependence can be solved by the proposed method.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2010. p. 9
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2937
Keywords
ARX- -Identification--Linear parameter-varying--Order selection
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-97548 (URN)LiTH-ISY-R-2937 (ISRN)
Available from: 2013-09-16 Created: 2013-09-16 Last updated: 2014-09-01Bibliographically approved
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