Advanced Mathematical Tools for Automatic Control Engineers, Volume 2: Stochastic Techniques provides comprehensive discussions on statistical tools for control engineers.

The book is divided into four main parts. Part I discusses the fundamentals of probability theory, covering probability spaces, random variables, mathematical expectation, inequalities, and characteristic functions. Part II addresses discrete time processes, including the concepts of random sequences, martingales, and limit theorems. Part III covers continuous time stochastic processes, namely Markov processes, stochastic integrals, and stochastic differential equations. Part IV presents applications of stochastic techniques for dynamic models and filtering, prediction, and smoothing problems. It also discusses the stochastic approximation method and the robust stochastic maximum principle.

• Provides comprehensive theory of matrices, real, complex and functional analysis
• Provides practical examples of modern optimization methods that can be effectively used in variety of real-world applications
• Contains worked proofs of all theorems and propositions presented

Table of Contents

PART I: Basics of Probability

Chapter 1. Probability Space

Chapter 2. Random Variables

Chapter 3. Mathematical Expectation

Chapter 4. Basic Probabilistic Inequalities

Chapter 5. Characteristic Functions

PART II: Discrete Time Processes

Chapter 6. Random Sequences

Chapter 7. Martingales

Chapter 8. Limit Theorems as Invariant Laws

PART Ill: Continuous Time Processes

Chapter 9. Basic Properties of Continuous Time Processes

Chapter 10. Markov Processes

Chapter 11. Stochastic Integrals

Chapter 12. Stochastic Differential Equations

PART IV: Applications

Chapter 13. Parametric Identification

Chapter 14. Filtering, Prediction and Smoothing

Chapter 15. Stochastic Approximation

Chapter 16. Robust Stochastic Control

Review

"This is a very well-written introduction to the basics of probability theory, stochastic analysis and their applications. Automatic control engineers will surely find much valuable material on different topics of modern and classical mathematics related to system and automatic control theories. In addition, this book may well serve as a reference book for researchers in applied probability theory and stochastic analysis…. Overall, this book is self-contained, well-organized, and clearly presented. It is a welcome addition to the existing collection of books in the field of probability and stochastic analysis, booth as a textbook at the graduate level and a reference book for researchers in this area." --Mathematical Reviews

About the Author

Alexander Poznyak is Professor and Department Head of Automatic Control at CINESTAV of IPN in Mexico. He graduated from Moscow Physical Technical Institute in 1970, and earned Ph.D. and Doctoral Degrees from the Institute of Control Sciences of Russian Academy of Sciences in 1978 and 1989, respectively. He has directed 43 Ph.D. theses, and published more than 260 papers and 14 books.