| 1. |
- Akcay, H., et al.
(author)
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On the choice of norms in system identification
- 1996
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In: IEEE Transactions on Automatic Control. - Linköping : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286. ; 41:9, s. 1367-1372
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Journal article (peer-reviewed)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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| 2. |
- Akçay, Hüseyin, et al.
(author)
-
On the Choice of Norms in System Identification
- 1994
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In: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; , s. 103-108
-
Reports (other academic/artistic)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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| 3. |
- Akçay, Hüseyin, et al.
(author)
-
The Least-Squares Identification of FIR Systems Subject to Worst-Case Noise
- 1993
-
Reports (other academic/artistic)abstract
- The least-squares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudo-random binary sequence. A lower bound on the worst-case transfer function error shows that the lest-square estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding trade-off in the random error case: with a worst-case formulation, the model complexity should not increase indefinitely as the size of the data set increases.
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| 4. |
- Akçay, Hüseyin, et al.
(author)
-
The Least-Squares Identification of FIR Systems Subject to Worst-Case Noise
- 1994
-
In: Proceedings of the 10th IFAC Symposium on System Identification. - Linköping : Linköping University. - 9780080422251 ; 23:5, s. 329-338
-
Reports (other academic/artistic)abstract
- The least-squares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudo-random binary sequence. A lower bound on the worst-case transfer function error shows that the least-square estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worst-case noise, the trade-off between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding trade-off in the random error case: with a worst-case formulation, the model complexity should not increase indefinitely as the size of the data set increases.
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| 5. |
- Barenthin, Märta, et al.
(author)
-
Gain estimation for Hammerstein systems
- 2006
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In: IFAC Proceedings Volumes (IFAC-PapersOnline). ; , s. 784-789
-
Conference paper (peer-reviewed)abstract
- In this paper, we discuss and compare three different approaches for L2- gain estimation of Hammerstein systems. The objective is to find the input signal that maximizes the gain. A fundamental difference between two of the approaches is the class, or structure, of the input signals. The first approach involves describing functions and therefore the class of input signals is sinusoids. In this case we assume that we have a model of the system and we search for the amplitude and frequency that give the largest gain. In the second approach, no structure on the input signal is assumed in advance and the system does not have to be modelled first. The maximizing input is found using an iterative procedure called power iterations. In the last approach, a new iterative procedure tailored for memoryless nonlinearities is used to find the maximizing input for the unmodelled nonlinear part of the Hammerstein system. The approaches are illustrated by numerical examples.
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| 6. |
- Gunnarsson, Svante, 1959-, et al.
(author)
-
Some Aspects of Iterative Identification and Control Design Schemes
- 1994
-
Reports (other academic/artistic)abstract
- In this report we study some different aspects of schemes for iterative identification and control design. By formulating the control objective as a criterion minimization task the problem of finding a model well suited for control appears to be closely related to a prediction error minimization problem in system identification. We discuss two ways of matching the control and identification criteria and evaluate their properties in simulations.
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| 7. |
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| 8. |
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| 9. |
- Gustafsson, Fredrik, et al.
(author)
-
Twenty-one ML estimators for model selection
- 1995
-
In: Automatica. - : Elsevier BV. - 0005-1098 .- 1873-2836. ; 31:10, s. 1377-1392
-
Journal article (peer-reviewed)abstract
- Classical approaches to determine a suitable model structure from observed input-output data are based on hypothesis tests and information-based criteria. Recently, the model structure has been considered as a stochastic variable, and standard estimation techniques have been proposed. The resulting estimators are closely related to the aforementioned methods. However, it turns out that there are a number of prior choices in the problem formulation, which are crucial for the estimators' behavior. The contribution of this paper is to clarify the role of the prior choices, to examine a number of possibilities and to show which estimators are consistent. This is done in a linear regression framework. For autoregressive models, we also investigate a novel prior assumption on stability, and give the estimator for the model order and the parameters themselves. Copyright © 1995 Elsevier Science Ltd All rights reserved.
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| 10. |
- Gustafsson, Fredrik, et al.
(author)
-
Twenty-One ML Estimators for Model Selection
- 1993
-
Reports (other academic/artistic)abstract
- Classical approaches to determine a suitable model structure from observed input-output data are based on hypothesis tests and information-based criteria. Recently, the model structure has been considered as a stochastic variable, and standard estimation techniques have been proposed. The resulting estimators are closely related to the aforementioned methods. However, it turns out that there are a number of prior choices in the problem formulation, which are crucial for the estimators' behavior. The contribution of this paper is to clarify the role of the prior choices, to examine a number of possibilities and to show which estimators are consistent. This is done in a linear regression framework. For autoregressive models, we also investigate a novel prior assumption on stability, and give the estimator for the model order and the parameters themselves.
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