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Exact and Approximate Modeling of Linear Systems: A Behavioral Approach elegantly introduces the behavioral approach to mathematical modeling.
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.
Table of contents:
Preface; 1. Introduction; 2. Approximate modeling via misfit minimization; Part I. Static Problems: 3. Weighted total least squares; 4. Structured total least squares; 5. Bilinear errors-in-variables model; 6. Ellipsoid fitting; Part II. Dynamic Problems: 7. Introduction to dynamical models; 8. Exact identification; 9. Balanced model identification; 10. Errors-in-variables smoothing and filtering; 11. Approximate system identification; 12. Conclusions; Appendices; Notation; Bibliography; Index.
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.
Table of contents:
Preface; 1. Introduction; 2. Approximate modeling via misfit minimization; Part I. Static Problems: 3. Weighted total least squares; 4. Structured total least squares; 5. Bilinear errors-in-variables model; 6. Ellipsoid fitting; Part II. Dynamic Problems: 7. Introduction to dynamical models; 8. Exact identification; 9. Balanced model identification; 10. Errors-in-variables smoothing and filtering; 11. Approximate system identification; 12. Conclusions; Appendices; Notation; Bibliography; Index.