Statistical Decision Theory in Adaptive Control Systems

Opis

Mathematics in Science and Engineering, Volume 39: Statistical Decision Theory in Adaptive Control Systems focuses on the combination of control theory with statistical decision theory.

This volume is divided into nine chapters. Chapter 1 reviews the history of control theory and introduces statistical decision theory. The mathematical description of random processes is covered in Chapter 2. In Chapter 3, the basic concept of statistical decision theory is treated, while in Chapter 4, the method of solving statistical decision problems is described. The application of statistical decision concepts to control problems is explained in Chapter 5. Chapter 6 elaborates a method of designing an adaptive control system. An application of the sequential decision procedure to the design of decision adaptive control systems is illustrated in Chapter 7. Chapter 8 is devoted to the description of a method of the adaptive adjustment of parameters contained in nonlinear control systems, followed by a discussion of the future problems in applications of statistical decision theory to control processes in the last chapter.

This book is recommended for students and researchers concerned with statistical decision theory in adaptive control systems.

Spis treści

Front Cover 2
Statistical Decision Theory in Adaptive Control Systems 7
Copyright Page 8
PREFACE 9
Table of Contents 13
CHAPTER 1. Introduction 17
- 1.1 Historical Development of Automatic Control 17
- 1.2 Control Systems and Stochastics 22
- 1.3 Adaptive Control and Decision Theory 23
CHAPTER 2. Mathematical Description of Random Processes 28
- 2.1 Introductory Remarks 28
- 2.2 Probability 29
- 2.4 Conditional Probability 33
- 2.3 Joint Probability 33
- 2.5 Bayes' Theorem 35

Front Cover 2
Statistical Decision Theory in Adaptive Control Systems 7
Copyright Page 8
PREFACE 9
Table of Contents 13
CHAPTER 1. Introduction 17
- 1.1 Historical Development of Automatic Control 17
- 1.2 Control Systems and Stochastics 22
- 1.3 Adaptive Control and Decision Theory 23
CHAPTER 2. Mathematical Description of Random Processes 28
- 2.1 Introductory Remarks 28
- 2.2 Probability 29
- 2.4 Conditional Probability 33
- 2.3 Joint Probability 33
- 2.5 Bayes' Theorem 35
- 2.6 Probability Distribution and Probability Density Function 37
- 2.7 Joint Probability Distribution and Joint Probability Density Function 41
- 2.8 Conditional Probability Distribution and Conditional Probability Density Function 44
- 2.9 Statistical Parameters of Random Variables 47
- 2.10 Stochastic Processes 55
- 2.11 Stationary Random Processes 58
- 2.12 Ergodic Hypothesis and Time Averages 60
- 2.13 Stationary Gaussian Random Processes 62
CHAPTER 3. Basic Concept of Statistical Decision Theory 66
- 3.1 Introductory Remarks 66
- 3.2 General Description of the Decision Situation 67
- 3.3 Signal Detection 71
- 3.4 Signal Extraction 72
CHAPTER 4. Evaluation Functions and Solutions in Statistical Decision Theory 74
- 4.1 Introductory Remarks 74
- 4.2 Basic Assumptions 74
- 4.3 General Formulation of Evaluation Functions in Decision Problems 77
- 4.4 Solutions of Decision Problems by the Bayes Criterion 79
- 4.5 Solutions of Binary Detection Problems 80
- 4.6 The Neyman-Pearson Detection Rule 85
CHAPTER 5. Statistical Decision Concept in Control Processes 88
- 5.1 Introductory Remarks 88
- 5.2 Decision Adaptive Control Systems under Preassigned Error Probabilities 94
- 5.3 Binary Decision Adaptive Control Systems Based on the Concept of the Sequential Test 96
- 5.4 Decision Adaptive Control Systems Based on the Neyman-Pearson Test 101
- 5.5 Ideal-Observer Decision-Making 104
CHAPTER 6. Nonsequential Decision Approaches in Adaptive Control Systems 107
- 6.1 Introductory Remarks 107
- 6.2 Extension of the Binary Detection Concept to N-ary Decision Problems 108
- 6.3 Derivation of the Bayesian System 111
- 6.4 Construction of a Decision System Subjected to Gaussian Random Noise 116
- 6.5 Decision-Making in System Identification 120
- 6.6 Decision-Making in System Identification with Gaussian Random Noise 124
- 6.7 Numerical Examples of Application of Decision Concept to Averaging Devices 133
- 6.8 Application of Decision Concept to Nondata Problems 144
CHAPTER 7. Sequential Decision Approaches in Adaptive Control Systems 149
- 7.1 Introductory Remarks 149
- 7.2 An Average Risk of Sequential Decision Procedure 149
- 7.3 Derivation of Bayes Solution 151
- 7.4 Application of Sequential Decision-Making to Adaptive Control Systems 155
- 7.5 Operating Characteristic Function (OC Function) and Average Sample Number Function (ASN Function) 159
- 7.6 Average Amount of Observation Time 169
- 7.7 Numerical Example 170
- 7.8 Comparison of Sequential and Nonsequential Decision Procedures 172
CHAPTER 8. Adaptive Adjustment of Parameters of Nonlinear Control Systems 177
- 8.1 Introductory Remarks 177
- 8.2 Application of Sequential Decision Rule 178
- 8.3 On-Off Relay Decision Control Systems 186
CHAPTER 9. Some Future Problems in Applications of Statistical Decision Theory to Control Processes 216
- 9.1 Introductory Remarks 216
- 9.2 Filtering Problems with Statistical Decision Theory 217
- 9.3 Present Status and Future Problems 225
Author Index 229
Subject Index 231

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