Abstract
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 identification 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 misfit between data and model is defined symmetrically in the system variables and measured in the ℓ ∞ or amplitude norm. With the introduction of proper notions of convergence, it is shown that the misfit 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 misfit function implies a consistent identification of optimal and suboptimal models.
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