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Exact and Approximate Modeling of Linear Systems: A Behavioral Approach illustrated edition [Pehme köide]

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  • Formaat: Paperback, 216 pages, kõrgus x laius x paksus: 229x152x13 mm, kaal: 402 g, illustrations
  • Sari: Mathematical Modeling and Computation No. 11
  • Ilmumisaeg: 31-Jan-2006
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898716039
  • ISBN-13: 9780898716030
Teised raamatud teemal:
Exact and Approximate Modeling of Linear Systems: A Behavioral Approach illustrated editionSuurem pilt
  • Formaat: Paperback, 216 pages, kõrgus x laius x paksus: 229x152x13 mm, kaal: 402 g, illustrations
  • Sari: Mathematical Modeling and Computation No. 11
  • Ilmumisaeg: 31-Jan-2006
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898716039
  • ISBN-13: 9780898716030
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780898716030.html
Märksõnad:
The behavioral approach to mathematical modeling presented in this text requires models to be viewed as sets of possible outcomes rather than to be a priori bound to particular representations. The authors, who are all from Katholieke Universiteit Leuven, Belgium, 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. The text 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. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)

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.

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.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.
Preface ix
Introduction
1(14)
Latency and misfit
1(1)
Data fitting examples
2(7)
Classical vs. behavioral and stochastic vs. deterministic modeling
9(1)
Chapter-by-chapter overview*
10(5)
Approximate Modeling via Misfit Minimization
15(12)
Data, model, model class, and exact modeling
15(2)
Misfit and approximate modeling
17(1)
Model representation and parameterization
18(1)
Linear static models and total least squares
19(2)
Nonlinear static models and ellipsoid fitting
21(2)
Dynamic models and global total least squares
23(1)
Structured total least squares
24(1)
Algorithms
25(2)
I Static Problems
27(70)
Weighted Total Least Squares
29(20)
Introduction
29(4)
Kernel, image, and input/output representations
33(2)
Special cases with closed form solutions
35(3)
Misfit computation
38(2)
Misfit minimization*
40(6)
Simulation examples
46(1)
Conclusions
47(2)
Structured Total Least Squares
49(20)
Overview of the literature
49(2)
The structured total least squares problem
51(3)
Properties of the weight matrix*
54(4)
Stochastic interpretation*
58(2)
Efficient cost function and first derivative evaluation*
60(4)
Simulation examples
64(4)
Conclusions
68(1)
Bilinear Errors-in-Variables Model
69(14)
Introduction
69(1)
Adjusted least squares estimatior of a bilinear model
70(2)
Properties of the adjusted least squares estimator*
72(2)
Simulation examples
74(1)
Fundamental matrix estimation
75(2)
Adjusted least squares estimation of the fundamental matrix
77(2)
Properties of the fundamental matrix estimator*
79(1)
Simulation examples
80(1)
Conclusions
80(3)
Ellipsoid Fitting
83(14)
Introduction
83(2)
Quadratic errors-in-variables model
85(1)
Ordinary least squares estimation
86(2)
Adjusted least squares estimation
88(3)
Ellipsoid estimation
91(1)
Algorithm for adjusted least squares estimation*
92(2)
Simulation examples
94(2)
Conclusions
96(1)
II Dynamic Problems
97(80)
Introduction to Dynamical Models
99(14)
Linear time-invariant systems
99(2)
Kernel representation
101(2)
Inputs, outputs, and input/output representation
103(1)
Latent variables, state variables, and state space representations
104(1)
Autonomous and controllable systems
105(1)
Representations for controllable systems
106(1)
Representation theorem
107(2)
Parameterization of a trajectory
109(1)
Complexity of a linear time-invariant system
110(1)
The module of annihilators of the behavior
111(2)
Exact Identification
113(26)
Introduction
113(2)
The most powerful unfalsified model
115(2)
Identifiability
117(1)
Conditions for identifiability
118(2)
Algorithms for exact identification
120(4)
Computation of the impulse response from data
124(4)
Realization theory and algorithms
128(2)
Computation of free responses
130(1)
Relation to subspace identification methods*
131(3)
Simulation examples
134(3)
Conclusions
137(2)
Balanced Model Identification
139(10)
Introduction
139(3)
Algorithm for balanced identification
142(1)
Alternative algorithms
143(1)
Splitting of the data into ``past'' and ``future''*
144(1)
Simulation examples
145(2)
Conclusions
147(2)
Errors-in-Variables Smoothing and Filtering
149(8)
Introduction
149(1)
Problem formulation
150(1)
Solution of the smoothing problem
151(2)
Solution of the filtering problem
153(2)
Simulation examples
155(1)
Conclusions
156(1)
Approximate System Identification
157(18)
Approximate modeling problems
157(3)
Approximate identification by structured total least squares
160(3)
Modifications of the basic problem
163(2)
Special problems
165(4)
Performance on real-life data sets
169(3)
Conclusions
172(3)
Conclusions
175(2)
A Proofs
177(6)
Weighted total least squares cost function gradient
177(1)
Structured total least squares cost function gradient
178(1)
Fundamental lemma
179(1)
Recursive errors-in-variables smoothing
180(3)
B Software
183(12)
Weighted total least squares
183(4)
Structured total least squares
187(3)
Balanced model identification
190(1)
Approximate identification
190(5)
Notation 195(2)
Bibliography 197(6)
Index 203
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.