Trends and Progress in System Identification - 1st Edition - ISBN: 9780080256832, 9781483148663

Trends and Progress in System Identification

1st Edition

Ifac Series for Graduates, Research Workers & Practising Engineers

Editors: Pieter Eykhoff
eBook ISBN: 9781483148663
Imprint: Pergamon
Published Date: 1st January 1981
Page Count: 418
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Description

Trends and Progress in System Identification is a three-part book that focuses on model considerations, identification methods, and experimental conditions involved in system identification. Organized into 10 chapters, this book begins with a discussion of model method in system identification, citing four examples differing on the nature of the models involved, the nature of the fields, and their goals. Subsequent chapters describe the most important aspects of model theory; the ""classical"" methods and time series estimation; application of least squares and related techniques for the estimation of dynamic system parameters; the maximum likelihood and error prediction methods; and the modern development of statistical methods. Non-parametric approaches, identification of nonlinear systems by piecewise approximation, and the minimax identification are then explained. Other chapters explore the Bayesian approach to system identification; choice of input signals; and choice and effect of different feedback configurations in system identification. This book will be useful for control engineers, system scientists, biologists, and members of other disciplines dealing withdynamical relations.

Table of Contents


0. Prologue

1. The Model Method

1 Necessity of Modeling

2 Principles of the Model Method

3 Phases in thee Elaboration of a Model

4 Examples

4.1 Modeling of Abiological System

4.2 Diagnosis of Jet - Engines

4.3 On-Line Identification of a Controlled Aircraft

4.4 Identification of a Multi-Variable Industrial Process

5 Where are the Difficulties?

6 Conclusions

References

2. Models: Equivalences, Uses, Extensions

1 Introduction

2 A "Gedanken Experiment"

3 Minimal Single-Input, Single-Output Models

4 Minimal Multi-Input, Multi-Output Models

5 Extensions of Model Carriers

6 Extensions of Model Structure

7 Conclusions

References

Identification Methods

3. "Classical" Methods and Time Series Estimation

1 "Classical" Methods

1.1 Frequency Analysis

1.2 Transient Analysis

1.3 Correlation Method

1.4 Standard Identification

2 Time Series Estimation

2.1 Discrete Model of Stationary Time Series

2.2 Analysis of the Autoregressive Process

2.3 Analysis of the Autoregressive-Moving Average Process

2.4 Some Applications to Linear System Identification

References

4. Least Squares and Regression Methods

1 Basic Concept

1.1 Introduction

1.2 Basic Relations

1.3 Analytic Solution of the Least Suqares

2 Recursive Solution of the Least Squares

2.1 Basic Relations

2.2 Increasing Number of Parameters

2.3 Geometrical Interpretations

3 Kalman-Bucy Filtering

3.1 State Estimation

3.2 Parameter Estimation by Kalman-Bucy Filter

3.3 Modified State Estimation Algorithms

4 Extension of Recursive Algorithms

4.1 Instrumental Variable Method (IV)

4.2 Generalized Least Squares (GLS)

4.3 Extended Least Squares (ELS)

4.4 Concluding Remarks

5 Discrete Square Root Filtering

5.1 Basic Square Root Procedure

5.2 Cholesky Algorithm

5.3 Exponential Forgetting

5.4 Modified Square Root Filtering

6 Applications of Least Squares

6.1 Examples of Least Squares Applications

6.2 Numerical Simulation Results

References

5. Maximum Likelihood and Prediction Error Methods

1 Introduction

2 The Maximum Likelihood Method

2.1 The Maximum Likelihood Function

2.2 The Likelihood Function

2.3 Independent Observations

2.4 Sequential Observations

2.5 Properties of the ML Estimates

2.6 Robustness

3 Estimating Parameters in Dynamical Systems

3.1 Problem Formulation

3.2 Evaluation of the Likelihood Function for a Prototype Problem

3.3 Prediction Error Formulation

3.4 Aspects on Algorithm Design

3.5 Computational Aspects

3.6 Constant Sampling Period

3.7 The ARMAX Model

3.8 Other Model Structures

3.9 Apriori Information, Bayesian Estimations

3.10 Commentary

4 Estimation Theory

4.1 Basic Concepts

4.2 Consistency

4.3 Approximative Models

4.4 Asymptotic Normality, Asymptotic Efficiency

4.5 Short Data Sets

4.6 Influence of the Prediction Horizon

4.7 Validation

5 Interactive Computing

6 Practical Aspects

6.1 The Standard Case

6.2 Bias

6.3 Elimination of Effects of Bias

6.4 Outliers

6.5 Time Delays

6.6 Quantization and Round-Off

6.7 Feedback

6.8 Conclusions

References

6. Modem Development of Statistical Methods

1 Introduction

2 The Basic Model

3 The Criterion

4 AIC as an Estimate of Neg-Entropy

5 Implication of MAICE for Identification

6 Practical Applications

7 Instrumental Models

8 Relation with other Procedures

9 Further Development

10 Conclusions

References

7. Extensions to Nonlinear and Minimax Approaches

1 Nonparametric Approaches

1.1 Introduction

1.2 Correlation Methods

1.3 Dispersion Methods

1.4 Resume

2 Identification of Nonlinear Processes by Piecewise Approximation

2.1 Statement of the Problem

2.2 Methods For Identification of Processes where Several Functioning Modes are Possible

2.3 Recurrent Piecewise Approximation Algorithms

2.4 Choice of Informative Input Variables; Hierarchical Piecewise Approximation

2.5 Experimental Study of Recurrence Piecewise Approximation Algorithms

2.6 Identification of Ethylene Polymerization

3 The Minimax Approach in Identification

3.1 Introduction

3.2 General Problem Statement

3.3 Minimax Identification with a least mean Squares Criterion

3.4 Minimax Identification with the Kolmogorov Criterion

3.5 Minimax Chi-Squared Identification

3.6 Minimax Identification with the Maximum Likelihood as the Criterion

3.7 Identifying Processes of Known Structure with a LMS Criterion

3.8 Identifying Processes of Unknown Structure

References

Appendix I

Appendix II

8 Bayesian Approach to System Identification

1 Introduction

2 Underlying Philosophy and Basic Relations

2.1 Two Basic Operations on Uncertainties

2.2 Independent Uncertain Quantities

2.3 Derived Relations

2.4 Additional Remarks

3 System Model, Re-Examined From Bayesian Viewpoint

3.1 Discrete White Noise

3.2 Measurable External Disturbances

4 Parameter Estimation and Output Prediction

4.1 Estimation in Closed Control Loop; Natural Conditions of Control

4.2 One-Shot Estimation

4.3 Problem of Initial Data

4.4 Non-Informative Priors and Principle of Stable Estimation

4.5 Redundant and Unidentifiable Parameters

4.6 Real-Time Estimation and Prediction

4.7 Sufficient Statistic and Self-Reproducing Forms of Probability Distributions

4.8 Generalized Multivariate Regression Model

5 Time-Varying Parameters and Adaptivity

5.1 Bayesian Viewpoint on Adaptivity

5.2 State Estimation and Output Prediction

5.3 Slowly Varying Parameters and Exponential Forgetting

6 System Classification

6.1 Model Classes and Hyptheses

6.2 Natural Conditions of Control in System Classification

6.3 Formal Solution of the Classification Problem

6.4 Role of Priors in Classification

6.5 Let Data Speak for Themselves

6.6. Application to Regression-Type Model Structures

Appendix A - Some Useful Lemmas from Matrix Algebra and Integral Calculus

Appendix B - FORTRAN Subroutine REFIL

References

EXPERIMENTAL CONDITIONS

9. Choice of Input Signals

1 Introduction

2 Historical Background

2.1 Engineering Literature

2.2 Statistical Literature

3 Statement of the Problem

4 Input Design Criteria

4.1 Parameter Space Criteria

4.2 Criteria in Output Space

5 Time-Domain Synthesis of Optimal Inputs

5.1 Application of Functional Analysis

5.2 Examples

5.3 Extension to Unknown Parameter in F

5.4 Extension to the Multi-Parameter Case

6 Frequency-Domain Synthesis of Optimal Inputs

7 Extensions

7.1 Continuous-Time Systems

7.2 Restricted Designs

7.3 State and Control Constraints

7.4 Nonlinear and Distributed Parameter Systems

7.5 Sequential and On-Line Input Design

7.6 Feedback Inputs

7.7 Extensions to other Criteria

7.8 Bounds

8 Examples

8.1 SISO Impulse Response Model with Stationary Input

8.2 Second-Order with Unknown Frequency

8.3 First-Order with Unknown Gains and Time Constant

8.4 Numerical Results

8.5 Input Design for Nonlinear Models of Catastrophe Theory: Heuristic Design

8.6 Input Design for Nonlinear Models of Catastrophe Theory: Optimal Results

8.7 Summary

8.8 Other Examples

9 Conclusions

References

10. Choice and Effect of Different Feedback Configurations

1 Introduction

2 Basic Concepts

2.1 Preliminaries

2.2 Basic Problems

2.3 Other Formulations and Problems

3 Identifiability and Measures of Accuracy

3.1 Identifiability

3.2 Criteria of Accuracy

4 Influence of the Identification Method on Identifiability and Accuracy

4.1 Influence on Identifiability

4.2 Influence on the Accuracy

5 Influence of the Model Structure on Identifiability and Accuracy

5.1 Influence on Identifiability

5.2 Influence on the Accuracy

6 Influence of Feedback on Identifiability and Accuracy

6.1 Influence on Identifiability

6.2 Influence on the Accuracy

6.3 Survey of other Contributions

7 Applications

7.1 Application to Ship Dynamics

7.2 Application to a Ball and Beam Process

8 Conclusions

References

Author Index

Subject Index




Details

No. of pages:
418
Language:
English
Copyright:
© Pergamon 1981
Published:
Imprint:
Pergamon
eBook ISBN:
9781483148663

About the Editor

Pieter Eykhoff