Tom Oomen


Research on Uncertainty Modeling

Problem

Any model is useless without a quantification of its uncertainty. This is particularly true for robust control techniques, which can generate a controller that works well for a system set, i.e., a nominal model and a bound on its uncertainty. A practically relevant way to represent such uncertainties is through cal{H}_infty norm-bounded perturbations. In our research, we have investigated several approaches to quantify uncertainty.

Validation-based uncertainty modeling

Model validation amounts to answering the question: can the model (including noise and uncertainty model) have generated the observed data? In our research, we have investigated this model validation for robust control question and have used it to quantify uncertainty. Due to its setting, this approach is particularly useful if you have many data sets under different operating conditions. Testing it a lot may give you confidence in the uncertain model.

A key aspect in such validation approaches is that they are typically optimistic, i.e., they tend to underestimate the size of uncertainty. We have developed an approach where we estimate and accurate noise model (nonparametrically) and then use the freedom in design of experiments to remove the optimism, and obtain a realistic size of uncertainty. The basic theory is reported in

It is successfully applied to several systems, including the ones reported in

Iteratively learning the mathcal{H}_infty norm

One of the aspects in uncertainty modeling for lightly damped systems is the fact that one often misses a resonance peak, or excites the system not exactly at the resonance frequency. If you have the freedom to do iterative experiments, the learning algorithms that we recently investigated for learning the mathcal{H}_infty norm of multivariable systems may be useful. The main motivation for doing this originates from uncertainty modeling for robust control, where an accurate bound on the model uncertainty is required. Results of this research are reported in

Local parametric modeling approaches

Recent developments in nonparametric modeling has led to new local parametric modeling techniques, in particular the local polynomial method and the local local rational method, which have recently been introduced in the identification community, have been applied to motion systems. Interestingly, these methods have only been used to enhance the estimate of FRFs on the DFT grid.

Recently, we have extended these methods to address the interpolation errors in uncertainty modeling. The results are reported in

Acknowledgement

The success of all the above work is due to the hard and excellent work of many people involved in this research, in particular the co-authors mentioned in the references.

Note that all figures shown on this page can be found in the mentioned papers. Please follow the guidelines regarding copyright and references when citing these.