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.

PrefaceChapter 1. Introduction 1.1 Historical Development of Automatic Control 1.2 Control Systems and Stochastics 1.3 Adaptive Control and Decision TheoryChapter 2. Mathematical Description of Random Processes 2.1 Introductory Remarks 2.2 Probability 2.3 Joint Probability 2.4 Conditional Probability 2.5 Bayes' Theorem 2.6 Probability Distribution and Probability Density Function 2.7 Joint Probability Distribution and Joint Probability Density Function 2.8 Conditional Probability Distribution and Conditional Probability Density Function 2.9 Statistical Parameters of Random Variables 2.10 Stochastic Processes 2.11 Stationary Random Processes 2.12 Ergodic Hypothesis and Time Averages 2.13 Stationary Gaussian Random ProcessesChapter 3. Basic Concept of Statistical Decision Theory 3.1 Introductory Remarks 3.2 General Description of the Decision Situation 3.3 Signal Detection 3.4 Signal ExtractionChapter 4. Evaluation Functions and Solutions in Statistical Decision Theory 4.1 Introductory Remarks 4.2 Basic Assumptions 4.3 General Formulation of Evaluation Functions in Decision Problems 4.4 Solutions of Decision Problems by the Bayes Criterion 4.5 Solutions of Binary Detection Problems 4.6 The Neyman-Pearson Detection RuleChapter 5. Statistical Decision Concept in Control Processes 5.1 Introductory Remarks 5.2 Decision Adaptive Control Systems under Preassigned Error Probabilities 5.3 Binary Decision Adaptive Control Systems Based on the Concept of the Sequential Test 5.4 Decision Adaptive Control Systems Based on the Neyman-Pearson Test 5.5 Ideal-Observer Decision-MakingChapter 6. Nonsequential Decision Approaches in Adaptive Control Systems 6.1 Introductory Remarks 6.2 Extension of the Binary Detection Concept to N-Ary Decision Problems 6.3 Derivation of the Bayesian System 6.4 Construction of a Decision System Subjected to Gaussian Random Noise 6.5 Decision-Making in System Identification 6.6 Decision-Making in System Identification with Gaussian Random Noise 6.7 Numerical Examples of Application of Decision Concept to Averaging Devices 6.8 Application of Decision Concept to Nondata ProblemsChapter 7. Sequential Decision Approaches in Adaptive Control Systems 7.1 Introductory Remarks 7.2 An Average Risk of Sequential Decision Procedure 7.3 Derivation of Bayes Solution 7.4 Application of Sequential Decision-Making to Adaptive Control Systems 7.5 Operating Characteristic Function (OC Function) and Average Sample Number Function (ASN Function) 7.6 Average Amount of Observation Time 7.7 Numerical Example 7.8 Comparison of Sequential and Nonsequential Decision ProceduresChapter 8. Adaptive Adjustment of Parameters of Nonlinear Control Systems 8.1 Introductory Remarks 8.2 Application of Sequential Decision Rule 8.3 On-Off Relay Decision Control SystemsChapter 9. Some Future Problems in Applications of Statistical Decision Theory to Control Processes 9.1 Introductory Remarks 9.2 Filtering Problems with Statistical Decision Theory 9.3 Present Status and Future ProblemsAuthor IndexSubject Index