Dynamic System Identification. Experiment Design and Data Analysis. Mathematics in Science and Engineering, Volume 136

✍ Scribed by Goodwin (editor)

• Publisher: Academic Press
• Year: 1977
• Tongue: English
• Leaves: 303
• Edition: 1
• Category: Library

✦ Table of Contents

Front Cover
Dynamic System Identification: Experiment Design and Data Analysis
Copyright Page
Contents
Preface
Chapter 1. Introduction and Statistical Background
1.1 Introduction
1.2 Probability Theory
1.3 Point Estimation Theory
1.4 Sufficient Statistics
1.5 Hypothesis Testing
1.6 The Bayesian Decision Theory Approach
1.7 Information Theory Approach
1.8 Commonly Used Estimators
1.9 Conclusions
Problems
Chapter 2. Linear Least Squares and Normal Theory
2.1 Introduction
2.2 The Least Squares Solution
2.3 Best Linear Unbiased Estimators
2.4 Unbiased Estimation of BLUE Covariance
2.5 Normal Theory
2.6 Numerical Aspects
2.7 Conclusions
Problems
Chapter 3. Maximum Likelihood Estimators
3.1 Introduction
3.2 The Likelihood Function and the ML Estimator
3.3 Maximum Likelihood for the Normal Linear Model
3.4 General Properties
3.5 Asymptotic Properties
3.6 The Likelihood Ratio Test
3.7 Conclusions
Problems
Chapter 4. Models for Dynamic Systems
4.1 Introduction
4.2 Deterministic Models
4.3 Canonical Models
4.4 Stochastic Models (The Covariance Stationary Case)
4.5 Stochastic Models (Prediction Error Formulation)
4.6 Conclusions
Problems
Chapter 5. Estimation for Dynamic Systems
5.1 Introduction
5.2 Least Squares for Linear Dynamic Systems
5.3 Consistent Estimators for Linear Dynamic Systems
5.4 Prediction Error Formulation and Maximum Likelihood
5.5 Asymptotic Properties
5.6 Estimation in Closed Loop
5.7 Conclusions
Problems
Chapter 6. Experiment Design
6.1 Introduction
6.2 Design Criteria
6.3 Time Domain Design of Input Signals
6.4 Frequency Domain Design of Input Signals
6.5 Sampling Strategy Design
6.6 Design for Structure Discrimination
6.7 Conclusions
Problems
Chapter 7. Recursive Algorithms
7.1 Introduction
7.2 Recursive Least Squares
7.3 Time Varying Parameters
7.4 Further Recursive Estimators for Dynamic Systems
7.5 Stochastic Approximation
7.6 Convergence of Recursive Estimators
7.7 Recursive Experiment Design
7.8 Stochastic Control
7.9 Conclusions
Problems
Appendix A. Summary of Results from Distribution Theory
A.1 Characteristic Function
A.2 The Normal Distribution

A.4 The “F“ Distribution
A.5 The Student t Distribution
A.6 The Fisher–Cochrane Theorem

Appendix B. Limit Theorems
B.1 Convergence of Random Variables
B.2 Relationships between Convergence Concepts
B.3 Some Important Convergence Theorems
Appendix C. Stochastic Processes
C.1 Basic Results
C.2 Continuous Time Stochastic Processes
C.3 Spectral Representation of Stochastic Processes
Appendix D. Martingale Convergence Results
D.1 Toeplitz and Kronecker Lemmas
D.2 Martingales
Appendix E. Mathematical Results
E.l Matrix Results
E.2 Vector and Matrix Differentiation Results
E.3 Caratheodory’s Theorem
Problem Solutions
References
Index