System Identification deals with building mathematical models from observations. The goal is to find a model y = G(s) u of the input-output behaviour of the system from measurements of the input signal u and the output signal y. This is an area of research is and has been very active internationally. The Automatic Control group has contributed to the area over several years, both in terms of theory, algorithms, applications and software.

The current activities concern

High dimensional data and dimension reduction

In several important applications, a large number of signals are measured. An example is fMRI (magnetic resonance imaging) experiments in medical applications where some 180 000 signals are measured each second. To deal with such problems it is necessary to reduce the dimension of the measurement space. We are investigation how LLE (local linear embedding) can be used for such problems and what relevance this approach has to dynamic system modeling.

Non-linear models

The perhaps most challenging problem in system identification today is to understand the possibilities and problems around estimating nonlinear models. One aspect is to develop new efficient methods, but it may be more important to understand fundamental problems, like how to test the presence of nonlinearities, to describe how linear models approximate nonlinear systems, and to provide a practical "user's guide" to all the choices available.

Applications to industrial robots

To estimate essential parameters associated with industrial robots is important both for controller design and tuning and for diagnosis purposes. An industrial robot is a nonlinear, complex system that typically operates in closed loop. This means that there are many challenges in obtaining effective and reliable methods.

Parameterisations and convex formulations

A typical approach to identification is to minimise a criterion of fit with respect to model parameters. These criteria are generally non-convex functions, and it is a important open problem to find ways to reparameterise and convexify the functions to be minimised.