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Exact and Approximate Modeling of Linear Systems: A Behavioral Approach (Mathematical Modeling and Computation) (Monographs on Mathematical Modeling and Computation): Ivan Markovsky, Jan C. Willems, Sabine Van Huffel, Bart De Moor

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.

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.

Book Description

Exact and Approximate Modeling of Linear Systems: A Behavioral Approach elegantly introduces the behavioral approach to mathematical modeling. 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.

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