Challenges of non-linear identification

Summary form only given. Identification of non-linear systems is an important problem in many applications. The topic is substantially richer than linear system identification. One reason for this is of course that the problem is significantly more difficult, but also that it has engaged several different research communities. With origins in statistical non-linear and non-parametric regression theory, areas like neural networks and learning theory can now be seen as research fields in their own right. In addition to the control field, many areas like artificial intelligence, pattern recognition, signal processing, oceanography, geology, etc, have developed their own approaches to the problem. This has lead to a very substantial literature on the topic. This talk will not attempt to give any survey of all approaches. It will focus on some core features of the problem, which represent the basic challenges. The foremost problem is the inherent lack of data support to build complex models. A black box model with n explaining variables (regressors) can be seen as a surface in Rⁿ⁺¹. Even for moderately large n, this is a huge space to fill with observations. The remedy would be to assume or look for sub-structures in the model/data, linearity in certain directions etc. For control applications it is natural to complement the data support with structures based on physical insights, "grey-box models". Interfacing physical modeling tools with identification techniques is thus important. Grey-box models, on other hand, typically lead to minimization problem with many local minima. This is another challenge, which possibly can be dealt with using modern computer algebra and optimization techniques.