1. 
 Akçay, Hüseyin, et al.
(författare)

On the Choice of Norms in System Identification
 1994

Rapport (övrigt vetenskapligt)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 lpnorms, p⩽2<∞ for F(C).


2. 
 Akçay, Hüseyin, et al.
(författare)

On the Choice of Norms in System Identification
 1996

Rapport (övrigt vetenskapligt)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 lpnorms, p⩽2<∞ for F(C).


3. 
 Akçay, Hüseyin, et al.
(författare)

On the Choice of Norms in System Identification
 1994

Ingår i: Proceedings of the 10th IFAC Symposium on System Identification.  9780080422251 ; s. 103108

Konferensbidrag (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 lpnorms, p⩽2<∞ for F(C).


4. 
 Akçay, Hüseyin, et al.
(författare)

The LeastSquares Identification of FIR Systems Subject to WorstCase Noise
 1993

Rapport (övrigt vetenskapligt)abstract
 The leastsquares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudorandom binary sequence. A lower bound on the worstcase transfer function error shows that the lestsquare estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worstcase noise, the tradeoff between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding tradeoff in the random error case: with a worstcase formulation, the model complexity should not increase indefinitely as the size of the data set increases.


5. 
 Akçay, Hüseyin, et al.
(författare)

The LeastSquares Identification of FIR Systems Subject to WorstCase Noise
 1994

Rapport (övrigt vetenskapligt)abstract
 The leastsquares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudorandom binary sequence. A lower bound on the worstcase transfer function error shows that the leastsquare estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worstcase noise, the tradeoff between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding tradeoff in the random error case: with a worstcase formulation, the model complexity should not increase indefinitely as the size of the data set increases.


6. 
 Akçay, Hüseyin, et al.
(författare)

The LeastSquares Identification of FIR Systems Subject to WorstCase Noise
 1994

Ingår i: Systems & control letters (Print).  01676911. ; 23:5, s. 329338

Tidskriftsartikel (refereegranskat)abstract
 The leastsquares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudorandom binary sequence. A lower bound on the worstcase transfer function error shows that the leastsquare estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worstcase noise, the tradeoff between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding tradeoff in the random error case: with a worstcase formulation, the model complexity should not increase indefinitely as the size of the data set increases.


7. 
 Akçay, Hüseyin, et al.
(författare)

The LeastSquares Identification of FIR Systems Subject to WorstCase Noise
 1994

Ingår i: Proceedings of the 10th IFAC Symposium on System Identification.  9780080422251 ; s. 8590

Konferensbidrag (refereegranskat)abstract
 The leastsquares identification of FIR systems is analyzed assuming that the noise is a bounded signal and the input signal is a pseudorandom binary sequence. A lower bound on the worstcase transfer function error shows that the lestsquare estimate of the transfer function diverges as the order of the FIR system is increased. This implies that, in the presence of the worstcase noise, the tradeoff between the estimation error due to the disturbance and the bias error (due to unmodeled dynamics) is significantly different from the corresponding tradeoff in the random error case: with a worstcase formulation, the model complexity should not increase indefinitely as the size of the data set increases.


8. 
 Ljung, Lennart, 1946, et al.
(författare)

Subspacebased Identification of Infinitedimensional Multivariable Systems from Frequencyresponse Data
 1996

Ingår i: Automatica.  Elsevier.  00051098. ; 32:6, s. 885902

Tidskriftsartikel (refereegranskat)abstract
 A new identification algorithm which identifies low complexity models of infinitedimensional systems from equidistant frequencyresponse data is presented. The new algorithm is a combination of the Fourier transform technique with the recent subspace techniques. Given noisefree data, finitedimensional systems are exactly retrieved by the algorithm. When noise is present, it is shown that identified models strongly converge to the balanced truncation of the identified system if the measurement errors are covariance bounded. Several conditions are derived on consistency, illustrating the tradeoffs in the selection of certain parameters of the algorithm. Two examples are presented which clearly illustrate the good performance of the algorithm.


9. 
 McKelvey, Tomas, et al.
(författare)

An Efficient Frequency Domain StateSpace Identification Algorithm : Robustness and Stochastic Analysis
 1994

Ingår i: Proceedings of the 33rd IEEE Conference on Decision and Control.  0780319680 ; s. 33483353 vol.4

Konferensbidrag (refereegranskat)abstract
 In this paper we present and analyze a novel algorithm for identifying linear timeinvariant discrete time statespace models from frequency response data. The algorithm is noniterative and exactly recovers a true system of order n, if n+2 noisefree uniformly spaced frequency response measurements are given. Analysis show that if the measurements are perturbed with errors upper bounded by ε the identification error will be upper bounded by ε and hence the algorithm is robust. An asymptotic stochastic analysis show, under weak assumptions, that the algorithm is consistent if the measurements are contaminated with noise.


10. 
 McKelvey, Tomas, et al.
(författare)

An Efficient Frequency Domain StateSpace Identification Algorithm Robustness and Stochastic Analyis
 1994

Rapport (övrigt vetenskapligt)abstract
 In this paper we present and analyze a novel algorithm for identifying linear timeinvariant discrete time statespace models from frequency response data. The algorithm is noniterative and exactly recovers a true system of order n, if n+2 noisefree uniformly spaced frequency response measurements are given. Analysis show that if the measurements are perturbed with errors upper bounded by ε the identification error will be upper bounded by ε and hence the algorithm is robust. An asymptotic stochastic analysis show, under weak assumptions, that the algorithm is consistent if the measurements are contaminated with noise.

