On continuity and consistency of l-infinite optimal models
Siep Weiland, Wolfgang Scherrer, Manfred Deistler · TU/e Research Portal · 1999
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.Neither the observed time series nor the set of candidate models are assumed to have an input-output structure.The misfit between data and model is defined symmetrically in the system variables and measured in the foo or amplitude norm.It is shown that the misfit function continuously depends on both the data and the identified model.The consequences of this result for consistency of optimal and suboptimal models are discussed.