Prof. Bo Wahlberg
Department of Signal, Sensors & Systems, Royal Institute of Technology, Stockholm, Sweden

Modelling and Identification with Rational Orthogonal Basis Functions

Models of dynamical systems are of great importance in almost all fields of science and engineering, and in particular in control and signal processing. System identification deals with the problem of estimating and validating such models from experimental data. By approximating the frequency response of a linear time-invariant system by a finite sum of exponentials, the problem of modeling and identification is considerably simplified. This corresponds to finite impulse response models in the time domain. However, by using instead infinite impulse response transfer functions as basis functions, much more efficient model structures can be obtain. Over the last decades a general theory has been developed which generalizes the work on Laguerre functions by Wiener in the 1930s, for the construction and analysis of general rational orthogonal basis functions models for the class of stable systems. The purpose of this presentation is to give an introduction and to discuss some recent applications in system identification of this theory. We will, in particular, discuss how to use orthogonal state-space realization theory and a certain transformation analysis to derive and analyze such models. The theory of rational orthogonal functions is closely related to certain reproducing kernel spaces. This connection can be used to analyze certain problems in system identification, and we will present some recent results in the input design based on these results.

Bo Wahlberg was born in Norrköping, Sweden, in 1959. He received a Ph.D. degree in 1987 from Linköping University, Sweden. In December 1991, he became Professor of the Chair of Automatic Control at the Royal Institute of Technology (KTH) in Stockholm, Sweden. He was a visiting professor at the Information Systems Lab, Stanford University, USA, August 1997-July 1998, and vice president for academic affairs at KTH 1999-2001. He is the head of Department of Signals, Sensors & Systems at KTH. Bo Wahlberg is currently the coordinator of European Research Network System Identification. His research interests include system identification, modeling and control of industrial processes, and signal processing with applications in communication and autonomous systems.