Today system identification is shifting from linear to nonlinear dynamical models. In existing nonlinear models there is a trade-off: either they are simple to compute but cannot be interpreted easily, such as black-box or nonparametric models, or they are elegant and simple, but they are hard to estimate, such as block-oriented models consisting of simple linear and nonlinear blocks.
In this thesis we will try to combine the advantages of both worlds by starting from a nonparametric Volterra series model, and develop methods to convert this to a block-oriented model. Possible questions that we will address involve structure detection, simplification of nonlinearities, model reduction, etc.
Insight into the nonlinear nature of a model simplifies both the modeling procedure as well as it improves user-interpretability.
The mathematical tools that we will consider are statistical estimation, matrix and tensor decompositions, polynomial approximation, regularization.
This topic has many open questions and both theoretical as applied research opportunities that can be adjusted to the interest of the student to get the right mix of theory and experiments. The ideal candidate has a keen interest in system identification and linear algebra.
Don’t hesitate to come and talk to Ivan Markovsky if you are interested!