Automatica, March 2005, Volume 41, No. 3


Introduction to the special issue on data-based modelling and system identification

System identification is a field of systems and control that has delivered powerful methods and tools for data-based system modelling. While the theory for identification of linear systems has become very mature, the challenges for the field are in modelling of more complex dynamical systems (nonlinear, distributed, hybrid, large scale), and in task-oriented issues (identification for control, diagnosis, detection, monitoring etc.).

The objective of this special issue is to present state-of-the-art results in data-based modelling and identification. In particular, the idea is to follow up on the many exciting results presented at the 13th IFAC Symposium on System Identification, SYSID-2003, held in Rotterdam, The Netherlands, August, 2003.

The call for papers for the special issue was very well received, and a total number of 96 papers were submitted. Due to time and space constraints it has been possible to accept and include in this special issue only a small subset of these submissions. However, several papers that could not be included in the special issue may appear in regular issues of Automatica.

In December 1995, the Automatica Special issue on Statistical Signal Processing and Control (edited by Björn Ottersten, Bo Wahlberg and Torsten Söderström) was published. It was to a large extent based on results presented at the 10th IFAC Symposium on System Identification, SYSID-94. It is now interesting to see how the field of system identification has evolved over the past ten years. For example, subspace methods in system identification were considered in the beginning of the nineties as a new promising research topic, and several ground-breaking papers appeared in the 1995 special issue.

The current special issue contains two papers on the current progress in subspace system identification:

D. Bauer: Asymptotic properties of subspace estimators

This paper surveys, ten year later, the state of art in asymptotic statistical analysis of such identification methods. The paper presents results on the asymptotic properties of estimators obtained using subspace methods. The main methods and tools are presented. It concludes by listing the main open questions and interesting research directions.

A. Chiuso and G. Picci: Consistency analysis of some closed-loop subspace identification methods

This paper gives a detailed presentation on subspace identification based on closed-loop experiments. The statistical consistency of two recently proposed subspace identification algorithms for closed-loop systems is analyzed. It is shown that both algorithms are biased due to an unavoidable mishandling of initial conditions, which occurs in closed loop identification.

Identification for control has been an extremely active research area in the last two decades, and there are two papers addressing this problem in the special issue:

H. Hjalmarsson: From experiment design to closed-loop control

This extensive paper, which is of both a tutorial and a survey type, explores the connection between identification and control, and in particular the design of low complexity controllers based on identified models from a statistical perspective. It is stressed that one should model as well as possible before any model or controller simplifications are made since this ensures the best statistical accuracy. Experiment design is a central issue, and the interaction between experimental constraints and performance specifications is studied in detail.

S. G. Douma and P. M. J. Van den Hof: Relations between uncertainty structures in identification for robust control

This paper studies the role of uncertainty description in identification for robust control. The uncertainty structure is very important when dealing with robust stability/performance analysis and robust synthesis of a controller. The main result is that an amplitude-bounded (circular) uncertainty set can equivalently be described in terms of an additive, Youla parameter and my-gap uncertainty. The result is used to design optimal experimental conditions in view of robust control design and in developing experiment-based robust control design methods.

Identification of nonlinear systems is a most challenging area. This special issue contains three papers in this area:

M. Enqvist and L. Ljung: Linear approximations of nonlinear FIR systems for separable input processes

This paper addresses the question of how to approximate nonlinear systems by linear ones. A necessary and sufficient separability condition on the (stochastic) input signal is presented that guarantees that a FIR representation of an LTI system optimally approximates a nonlinear system. The result is applied to the structure identification of systems and the identification of generalized Wiener-Hammerstein models.

J. Roll, A. Nazin and L. Ljung: Nonlinear system identification via direct weight optimization

This paper proposes a general framework for nonlinear system identification. The authors' method amounts to postulating an estimator that is linear in the observed outputs, and optimize a weighted min-max type criterion to update the estimation. The approach leads to novel identification algorithms and is applied to various nonlinear dynamical systems.

J. Schoukens, R. Pintelon, T. Dobrowiecki and Y. Rolain: Identification of linear systems with nonlinear distortions

The effect of nonlinear distortions for system identification is considered in this paper. Excitations are supposed to belong to various classes of periodic inputs, a classical linear least squares estimate is performed and the residue is detected, qualified and quantified in terms of odd and even moments.

The issues of identifiability and model structures are addressed in the following papers:

L. Belkoura: Identifiability of systems described by convolution equations

This paper studies parameter identifiability for a class of finite and infinite dimensional systems described by convolution equations. Identifiability is also analyzed from knowledge of solutions on a bounded time interval.

R. L. M. Peeters and B. Hanzon: Identifiability of homogeneous systems using the state isomorphism approach

This paper presents a state isomorphism approach to global identifiability analysis of parameterized classes of nonlinear state space systems with specified initial states. In particular the class of homogeneous systems is investigated.

T. Ribarits, M. Deistler and B. Hanzon: An analysis of separable least squares data driven local coordinates for maximum likelihood estimation of linear systems

This paper studies separable least squares data driven local coordinates applied to maximum likelihood estimation of linear dynamic systems. Insights into the geometry and topology are given, together with the result that the separable least squares methodology is applicable to maximum likelihood estimation of linear dynamic systems.

F. Rosenqvist and A. Karlström: Realisation and estimation of piecewise-linear output-error models

Piecewise-linear systems in input/output form with instant and delayed switching schedules are analysed. It is shown that it is possible to find state-space models for such representations. Additionally a prediction-error minimization (PEM) method for piecewise-linear output-error predictors is derived.

The final paper of the special issue is:

V. K. Chitrakaran, D. M. Dawson, W. E. Dixon and J. Chen: Identification of a moving object's velocity with a fixed camera

This paper studies a continuous estimator strategy to asymptotically identify the six degree-of-freedom velocity of a moving object using a single fixed camera. The design of the estimator is based on the fusion of homography-based techniques with Lyapunov design methods.

We hope that this special issue will contribute to advancing knowledge in system identification. It confirms that system identification is still a very active field of research.

We would also like to take this opportunity to thank all authors who have submitted papers to the special issue, and the many reviewers involved in the refereeing of the submissions.

Torsten Söderström, Paul Van den Hof, Bo Wahlberg, Siep Weiland
Guest Editors