On the choice of norms in system identification

• 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 ≀ 2 < ∞ for F(C). ©1996 IEEE.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Keyword

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

Publication and Content Type

ref (subject category)

art (subject category)