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Exact and Approximate Modeling of Linear Systems: A Behavioral ApproachExact and Approximate Modeling of Linear Systems: A Behavioral Approach

Ivan Markovsky, Jan C. Willems, Sabine Van Huffel, and Bart De Moor



Mathematical Modeling and Computation 11

Exact and Approximate Modeling of Linear Systems: A Behavioral Approach elegantly introduces the behavioral approach to mathematical modeling, an approach that requires models to be viewed as sets of possible outcomes rather than to be a priori bound to particular representations. The authors discuss exact and approximate fitting of data by linear, bilinear, and quadratic static models and linear dynamic models, a formulation that enables readers to select the most suitable representation for a particular purpose.

This book presents exact subspace-type and approximate optimization-based identification methods, as well as representation-free problem formulations, an overview of solution approaches, and software implementation. Readers will find an exposition of a wide variety of modeling problems starting from observed data. The presented theory leads to algorithms that are implemented in C language and in MATLAB.

Audience
This book is written primarily for electrical, mechanical, and chemical engineers, applied mathematicians, econometricians, and statisticians. Chapters 3 and 4 will be of interest to chemometricians, and Chapters 5 and 6 to researchers in the field of computer vision.

About the Authors
Ivan Markovsky is a Postdoctoral Researcher of Electrical Engineering at Katholieke Universiteit Leuven, Belgium. His current research work is focused on identification methods in the behavioral setting and errors-in-variables estimation problems.

Jan C. Willems is a full-time Visiting Professor of Electrical Engineering at Katholieke Universiteit Leuven, Belgium, with the research group on Signals, Identification, System Theory, and Automation (SISTA). His interests lie mainly in modeling, identification, control, and issues related to the foundations of systems theory.

Sabine Van Huffel is a Professor of Electrical Engineering at Katholieke Universiteit Leuven, Belgium. Her research interests are in signal processing, numerical linear algebra, errors-in-variables regression, system identification, pattern recognition, (non)linear modeling, software, and statistics applied to biomedicine.

Bart De Moor is a Professor of Electrical Engineering at Katholieke Universiteit Leuven, Belgium. His research interests are in numerical linear algebra and optimization, system theory, control and identification, quantum information theory, data mining, information retrieval, and bioinformatics.

Contents
Preface; Chapter 1: Introduction; Chapter 2: Approximate Modeling via Misfit Minimization; Part I: Static Problems; Chapter 3: Weighted Total Least Squares; Chapter 4: Structured Total Least Squares; Chapter 5: Bilinear Errors-in-Variables Model; Chapter 6: Ellipsoid Fitting; Part II: Dynamic Problems; Chapter 7: Introduction to Dynamical Models; Chapter 8: Exact Identification; Chapter 9: Balanced Model Identification; Chapter 10: Errors-in-Variables Smoothing and Filtering; Chapter 11: Approximate System Identification; Chapter 12: Conclusions
Appendix A: Proofs; Appendix B: Software;
Notation; Bibliography; Index

2006 / x + 206 pages / Softcover / ISBN-13: 978-0-898716-03-0 / ISBN-10: 0-89871-603-9 /
List Price $71.50 / SIAM Member Price $50.05 / Order Code MM11
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