On the choice of norms in system identification

NR 20140805
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 â„“p-norms, p â‰€ 2 < âˆž for F(C). Â©1996 IEEE.

TEKNIK OCH TEKNOLOGIER Elektroteknik och elektronik Reglerteknik hsv//swe
ENGINEERING AND TECHNOLOGY Electrical Engineering, Electronic Engineering, Information Engineering Control Engineering hsv//eng
Convergence of numerical methods
Mathematical models
Robustness (control systems)
Statistical methods
Parameter estimate variance
Prediction error system
Identification (control systems)
SRA - ICT
SRA - Informations- och kommunikationsteknik
Automatic control

Hjalmarsson, Håkan,1962-Linköpings universitet,Reglerteknik,Tekniska högskolan(Swepub:kth)u10a8l40 (author)
Ljung, Lennart,1946-Linköpings universitet,Reglerteknik,Tekniska högskolan(Swepub:liu)lenlj48 (author)
Linköpings universitetReglerteknik (creator_code:org_t)

In:IEEE Transactions on Automatic ControlLinköping : Institute of Electrical and Electronics Engineers (IEEE)41:9, s. 1367-13720018-9286

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