On the role of exact models in approximate modeling problems

S. Weiland; A.A. Stoorvogel

doi:10.1109/CDC.1996.574432

On the role of exact models in approximate modeling problems

S. Weiland, A.A. Stoorvogel

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

4 Citations (Scopus)

Abstract

The behavioral theory of dynamical system is used to address a deterministic system identification problem with a newly defined measure of misfit between data and linear time-invariant systems. An approximate model identification problem is formalized using this misfit criterium. In particular, Pareto optimal models are defined as feasible trade-offs between low complexity and low misfit models. The main result of this paper provides a complete characterization of bounded misfit and bounded complexity models. It is shown that this entire class of approximate models corresponds to the set of most powerful unfalsified models of reduced data sets. The reduced data sets are derived from Hankel norm approximations of the data. The main result therefore emphasizes the relevance of the exact modeling problem for the identification of approximate systems. The set of all Pareto optimal models is characterized as a simple consequence of this result.

Original language	English
Title of host publication	Proceedings 35th IEEE Conference on Decision and Control (Kobe, Japan, December 11-13, 1996)
Place of Publication	New York
Publisher	Institute of Electrical and Electronics Engineers
Pages	700-705
ISBN (Print)	0-7803-3590-2
DOIs	https://doi.org/10.1109/CDC.1996.574432
Publication status	Published - 1996

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title = "On the role of exact models in approximate modeling problems",

abstract = "The behavioral theory of dynamical system is used to address a deterministic system identification problem with a newly defined measure of misfit between data and linear time-invariant systems. An approximate model identification problem is formalized using this misfit criterium. In particular, Pareto optimal models are defined as feasible trade-offs between low complexity and low misfit models. The main result of this paper provides a complete characterization of bounded misfit and bounded complexity models. It is shown that this entire class of approximate models corresponds to the set of most powerful unfalsified models of reduced data sets. The reduced data sets are derived from Hankel norm approximations of the data. The main result therefore emphasizes the relevance of the exact modeling problem for the identification of approximate systems. The set of all Pareto optimal models is characterized as a simple consequence of this result.",

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On the role of exact models in approximate modeling problems. / Weiland, S.; Stoorvogel, A.A.

Proceedings 35th IEEE Conference on Decision and Control (Kobe, Japan, December 11-13, 1996). New York : Institute of Electrical and Electronics Engineers, 1996. p. 700-705.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Stoorvogel, A.A.

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AB - The behavioral theory of dynamical system is used to address a deterministic system identification problem with a newly defined measure of misfit between data and linear time-invariant systems. An approximate model identification problem is formalized using this misfit criterium. In particular, Pareto optimal models are defined as feasible trade-offs between low complexity and low misfit models. The main result of this paper provides a complete characterization of bounded misfit and bounded complexity models. It is shown that this entire class of approximate models corresponds to the set of most powerful unfalsified models of reduced data sets. The reduced data sets are derived from Hankel norm approximations of the data. The main result therefore emphasizes the relevance of the exact modeling problem for the identification of approximate systems. The set of all Pareto optimal models is characterized as a simple consequence of this result.

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