Infinite and finite sample properties of set membership identification in a stochastic setting

Wataru Kitamura; Yasumasa Fujisaki; Er-Wei Bai

doi:10.1109/CDC.2002.1184503

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Conference proceeding

Infinite and finite sample properties of set membership identification in a stochastic setting

Wataru Kitamura, Yasumasa Fujisaki and Er-Wei Bai

Proceedings of the 41st IEEE Conference on Decision and Control, 2002, Vol.1, pp.269-274

2002

DOI: 10.1109/CDC.2002.1184503

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Abstract

In this paper, infinite and finite sample properties of set membership identification are investigated in a stochastic setting. In particular, the size of the membership set in the presence of not only disturbance but also parameter uncertainty is estimated. The bounds of the disturbance and the parameter uncertainty are assumed to be tight as well as known, where tight means that the disturbance and the parameter uncertainty take a value around their extreme points with nonzero probability. The following results are obtained. (i) Infinite sample case: The size of the membership set converges to zero with probability one as the number of samples tends to infinity if the regressor is persistently exciting and the bounds of the disturbance and the parameter uncertainty are tight. This means that the membership set converges to the true but unknown parameter. (ii) Finite sample case: For a given number of samples, the size of the membership set can be estimated with a probabilistic confidence if the regressor is periodic and persistently exciting, and the bounds of the disturbance and the parameter uncertainty are tight. This result also clarifies the necessary number of samples such that the size of the membership set is less than a specified bound with a specified probability.

Cities and towns

Discrete time systems

H infinity control

Marine vehicles

Size measurement

Stochastic processes

Stochastic systems

Systems engineering and theory

Uncertain systems

Uncertainty

Details

Title: Subtitle: Infinite and finite sample properties of set membership identification in a stochastic setting
Creators: Wataru Kitamura - Kobe University
Yasumasa Fujisaki - Kobe University
Er-Wei Bai - Electrical and Computer Engineering
Resource Type: Conference proceeding
Publication Details: Proceedings of the 41st IEEE Conference on Decision and Control, 2002, Vol.1, pp.269-274
Publisher: IEEE
DOI: 10.1109/CDC.2002.1184503
ISSN: 0191-2216
Language: English
Date published: 2002
Academic Unit: Electrical and Computer Engineering
Record Identifier: 9984573819302771

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