NONLINEAR BLACK-BOX MODELING IN SYSTEM-IDENTIFICATION - A UNIFIED OVERVIEW

A nonlinear black-box structure for a dynamical system is a model stru cture that is prepared to describe virtually any nonlinear dynamics. T here has been considerable recent interest in this area, with structur es based on neural networks, radial basis networks, wavelet networks a nd hinging hyperplanes, as well as wavelet-transform-based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, t he choices that have to be made and what considerations are relevant f or a successful system-identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a conc atenation of a mapping form observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually form ed as a basis function expansion. The basis functions are typically fo rmed from one simple scalar function, which is modified in terms of sc ale and location. The expansion from the scalar argument to the regres sor space is achieved by a radial- or a ridge-type approach, Basic tec hniques for estimating the parameters in the structures are criterion minimization, as well as two-step procedures, where first the relevant basis functions are determined, using data, and then a linear least-s quares step to determine the coordinates of the function approximation . A particular problem is to deal with the large number of potentially necessary parameters. This is handled by making the number of 'used' parameters considerably less than the number of 'offered' parameters, by regularization, shrinking, pruning or regressor selection.