Nonlinear Black-Box Modeling in System Identification

This paper describes the common framework for these approaches. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping from 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 formed as a basis function expansion. The basis functions are typically formed from one simple scalar function which is modified in terms of scale and location. The expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach. Basic techniques 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 squares 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. A more comprehensive treatment is given in [8] and [4]. 2 System Identificatio