Identification of structured models for nonlinear systems

The control community makes use of mathematical models intensively to design high quality controllers. These mathematical models are often obtained from first principles, making use of detailed knowledge about the physical laws that describe systems. The major advantage of such an approach is that it provides detailed physical models that give much insight into the problems studied, however, at the cost of a long and difficult modeling process. At the other end of the possible modeling strategies we find the data-driven approach, where all information is retrieved from experimental data. These models are called black box models, and it is usually less expensive and less time-consuming to get them. System identification theory was developed to address the need for good methods to estimate mathematical models from noisy data. Nowadays mature and inexpensive tools are available to derive good models for linear dynamic systems. However, many systems are nonlinear so that more advanced tools are needed. Nonlinear models are significantly more complex than linear models. This does not only affect the interpretability of the estimated model, also the model structure selection problem becomes more difficult. In this presentation I like to illustrate these problems and discuss some possibilities to address the new challenges. A number of nonlinear modeling strategies will be discussed, considering unstructured and highly structured models.