A deterministic approach to approximate modelling of input-output data

The problem of system identification is reconsidered as a problem of deterministic approximate modeling on the basis of input-output data. In the approach presented, system identification methods are required to yield models that are well defined, in the sense that the models obtained proceed from the available data sequence and from specified users´ choices, and not from implicit (statistical) assumptions about the data and the underlying process. On the basis of the system-theoretic concept of dynamical system behavior, a framework is developed in which the identification problem as considered above can be formulated properly. In this framework the different components of an identification method-model set, parameterization, and identification criterion-are defined in a fundamental and natural way. A clear distinction is made between the problems of identification and parameterization. For the popular class of equation error identification methods, it is shown that the construction of parameterizations that are identifiable by a least-squares identification criterion requires specific users´ choices that have not been recognized before and that influence the optimal models obtained