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| 2. |
- Akcay, H., et al.
(författare)
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On the choice of norms in system identification
- 1996
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Ingår i: IEEE Transactions on Automatic Control. - Linköping : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286. ; 41:9, s. 1367-1372
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C > 0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all ℓp-norms, p ≀ 2 < ∞ for F(C). ©1996 IEEE.
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| 3. |
- Akçay, Hüseyin, et al.
(författare)
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On the Choice of Norms in System Identification
- 1994
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Ingår i: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; , s. 103-108
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we discuss smooth and sensitive norms for prediction error system identification when the disturbances are magnitude bounded. Formal conditions for sensitive norms, which give an order of magnitude faster convergence of the parameter estimate variance, are developed. However, it also is shown that the parameter estimate variance convergence rate of sensitive norms is arbitrarily bad for certain distributions. A necessary condition for a norm to be statistically robust with respect to the family F(C) of distributions with support [-C, C] for some arbitrary C>0 is that its second derivative does not vanish on the support. A direct consequence of this observation is that the quadratic norm is statistically robust among all lp-norms, p⩽2<∞ for F(C).
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| 4. |
- Barenthin Syberg, Märta, 1979-
(författare)
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Complexity Issues, Validation and Input Design for Control in System Identification
- 2008
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- System identification is about constructing and validating modelsfrom measured data. When designing system identificationexperiments in control applications, there are many aspects toconsider. One important aspect is the choice of model structure.Another crucial issue is the design of input signals. Once a modelof the system has been estimated, it is essential to validate theclosed loop performance if the feedback controller is based onthis model. In this thesis we consider the prediction-erroridentification method. We study model structure complexity issues,input design and model validation for control. To describe real-life systems with high accuracy, models of veryhigh complexity are typically needed. However, the variance of themodel estimate usually increases with the model order. In thisthesis we investigate why system identification, despite thisrather pessimistic observation, is successfully applied in theindustrial practise as a reliable modelling tool. It is shown thatby designing suitable input signals for the identificationexperiment, we obtain accurate estimates of the frequency functionalso for very complex systems. The input power spectrum can beused to shape the model quality. A key tool in input design is tointroduce a linear parametrization of the spectrum. With thisparametrization, several optimal input design problems can berewritten as convex optimization problems. Another problem considered is to design controllers withguaranteed robust stability and prescribed robust performanceusing models identified from experimental data. These models areuncertain due to process noise, measurement noise and unmodelleddynamics. In this thesis we only consider errors due tomeasurement noise. The model uncertainty is represented byellipsoidal confidence regions in the model parameter space. Wedevelop tools to cope with these ellipsoids for scalar andmultivariable models. These tools are used for designing robustcontrollers, for validating the closed loop performance and forimproving the model with input design. Therefore this thesis ispart of the research effort to connect prediction-erroridentification methods and robust control theory. The stability of the closed loop system can be validated using thesmall gain theorem. A critical issue is thus to have an accurateestimate of the L2-gain of the system. The key tosolve this problem is to find the input signal that maximizes thegain. One approach is to use a model of the system to design theinput signal. An alternative approach is to let the system itselfdetermine a suitable input sequence in repeated experiments. Insuch an approach no model of the system is required. Proceduresfor gain estimation of linear and nonlinear systems are discussedand compared.
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| 5. |
- Galrinho, Miguel
(författare)
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Least Squares Methods for System Identification of Structured Models
- 2016
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The purpose of system identification is to build mathematical models for dynamical systems from experimental data. With the current increase in complexity of engineering systems, an important challenge is to develop accurate and computationally efficient algorithms.For estimation of parametric models, the prediction error method (PEM) is a benchmark in the field. When the noise is Gaussian and a quadratic cost function is used, PEM provides asymptotically efficient estimates if the model orders are correct. A disadvantage with PEM is that, in general, it requires minimizing a non-convex function. Alternative methods are then needed to provide initialization points for the optimization. Two important classes of such methods are subspace and instrumental variables.Other methods, such as Steiglitz-McBride, use iterative least squares to avoid the non-convexity of PEM. This thesis focuses on this class of methods, with the purpose of addressing common limitations in existing algorithms and suggesting more accurate and computationally efficient ones. In particular, the proposed methods first estimate a high order non-parametric model and then reduce this estimate to a model of lower order by iteratively applying least squares.Two methods are proposed. First, the weighted null-space fitting (WNSF) uses iterative weighted least squares to reduce the high order model to a parametric model of interest. Second, the model order reduction Steiglitz-McBride (MORSM) uses pre-filtering and Steiglitz-McBride to estimate a parametric model of the plant. The asymptotic properties of the methods are studied, which show that one iteration provides asymptotically efficient estimates. We also discuss two extensions for this type of methods: transient estimation and estimation of unstable systems.Simulation studies provide promising results regarding accuracy and convergence properties in comparison with PEM.
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| 6. |
- Hjalmarsson, Håkan, 1962-, et al.
(författare)
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A Unifying View of Disturbances in Identification
- 1994
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Ingår i: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; , s. 73-78
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Konferensbidrag (refereegranskat)
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| 7. |
- Hjalmarsson, Håkan, 1962-, et al.
(författare)
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Assessing model quality from data
- 1991
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Ingår i: Modeling, estimation and control of systems with uncertainty. - : Birkhäuser Verlag. ; , s. 167-187
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Bokkapitel (refereegranskat)
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| 8. |
- Hjalmarsson, Håkan, et al.
(författare)
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Assessing Model Quality from Data
- 1991
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Ingår i: Proceedings of the 1990 IIASA Symposium on Modeling and Control of Systems with Uncertainty. - Linköping : Linköping University. - 9781461204435 ; , s. 167-187
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The problem of deriving error bounds for estimated transfer functions is addressed. By blending a priori knowledge and information obtained from measured data, we show how the uncertainty of transfer function estimates can be quantified. The emphasis is on errors due to model mismatch. The effects of unmodeled dynamics can be considered as bounded disturbances. Hence, techniques from set membership identification can be applied to this problem. The approach taken corresponds to weighted least squares estimation, and provides hard frequency domain transfer function error bounds.Real processes rarely are time-invariant. Hence, the unmodeled dynamics contains a time-varying part. It is important to quantify this model error as well. Herein, this is done in terms of confidence bounds for the “frozen” transfer function, i.e. the sequence of transfer functions obtained when freezing the time variable at succesive times. This method is based on the assumption that the true system is varying around some nominal system.
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| 9. |
- Hjalmarsson, Håkan, 1962-, et al.
(författare)
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Discussion of `unknown-but-bounded' disturbances in system identification
- 1993
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Ingår i: Proceedings of the IEEE Conference on Decision and Control. - San Antonio, TX, USA : Linköping University. - 0780312988 ; , s. 535-536
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Konferensbidrag (refereegranskat)abstract
- In this contribution we point out that a fundamental property of a disturbance is that it is independent of the input - otherwise it is rather part of the system. Based on this characterization we show that parameter convergence can be obtained not only for stochastic but also for unknown-but-bounded disturbances if the input is at our disposal.
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| 10. |
- Hjalmarsson, Håkan, 1962-, et al.
(författare)
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Estimating model variance in the case of undermodeling
- 1992
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Ingår i: IEEE Transactions on Automatic Control. - Linköping : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523. ; 37:7, s. 1004-1008
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Tidskriftsartikel (refereegranskat)abstract
- A reliable quality estimate of a given model is a prerequisite for any reasonable use of the model. The model error consists of two different contributions: the bias error and the random error. In this contribution, it is shown that the size (variance) of the random error can be reliably estimated in the case where a true system description cannot be achieved in the model structure used. This consistent error estimate can differ considerably from the conventionally used variance estimate, which could thus be misleading.
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