𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On continuity and consistency of ℓ∞ optimal models

✍ Scribed by Siep Weiland; Wolfgang Scherrer; Manfred Deistler

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
148 KB
Volume
44
Category
Article
ISSN
0167-6911

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✦ Synopsis

This paper is concerned with the question of continuity of the mapping from observed time series to models. The behavioral framework is adopted to formalize a model identiÿcation problem in which the observed time series is decomposed into a part explained by a model and a remaining part which is ascribed to noise. The misÿt between data and model is deÿned symmetrically in the system variables and measured in the '∞ or amplitude norm. With the introduction of proper notions of convergence, it is shown that the misÿt function continuously depends on both the data and the model. Two notions of consistency are formalized and it is shown that the continuity of the misÿt function implies a consistent identiÿcation of optimal and suboptimal models.

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