Exact and Approximate Modeling of Linear Systems: A Behavioral Approach

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.