A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, 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 di erent approaches, the choices that have to be made and what considerations are relevant for a successful system identi cation application of these techniques. 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 modi ed 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 rst 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 \o ered" parameters, by regularization, shrinking, pruning or regressor selection. A more mathematically comprehensive treatment i s g i v en in a companion paper (Juditsky et al., 1995).

The links between identification and control are examined. The main trends in this research area are summarized, with particular focus on the design of low complexity controllers from a statistical perspective. It is argued that a guiding principle should be to model as well as possible before any model or controller simplifications are made as this ensures the best statistical accuracy. This does not necessarily mean that a full-order model always is necessary as well designed experiments allow for restricted complexity models to be near-optimal. Experiment design can therefore be seen as the key to successful applications. For this reason, particular attention is given to the interaction between experimental constraints and performance specifications.

Adaptive and iterative control algorithms based on explicit criterion minimization are briefly reviewed and an overview of one such algorithm, iterative feedback tuning (IFT) , is presented. The basic IFT algorithm is reviewed for both single-input/single-output and multi-input/multi-output systems. Subsequently the application to non-linear systems is discussed. Stability and robustness aspects are covered. A survey of existing extensions, applications and related methods is also provided. ; 16:373-395 H. HJALMARSSON Sensitivity modelsLater it was recognized that for linear time-invariant, processes, the sensitivity of any signal, sðtÞ say, in the system w.r.t. any scalar parameter r in the system, i.e. the partial derivative @sðtÞ=@r;

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