The Second Volume of this work continues the approach of the First Volume, providing mathematical tools for the control engineer and examining such topics as random variables and sequences, iterative logarithmic and large number laws, differential equations, stochastic measurements and optimization, discrete martingales and probability space. Included are proofs of all theorems and contains many examples with solutions. Written for researchers, engineers and advanced students who wish to increase their familiarity with different topics of modern and classical mathematics related to system and automatic control theories. It is written for researchers, engineers and advanced students who wish to increase their familiarity with different topics of modern and classical mathematics related to system and automatic control theories with applications to game theory, machine learning and intelligent systems.
Content:
Front Matter
• Notations and Symbols
• List of Figures
• List of Tables
• Preface
• Table of Contents
•Part I. Basics of Probability 1. Probability Space
2. Random Variables
3. Mathematical Expectation
4. Basic Probabilistic Inequalities
5. Characteristic Functions
•Part II. Discrete Time Processes 6. Random Sequences
7. Martingales
8. Limit Theorems as Invariant Laws
•Part III. Continuous Time Processes 9. Basic Properties of Continuous Time Processes
10. Markov Processes
11. Stochastic Integrals
12. Stochastic Differential Equations
•Part IV. Applications 13. Parametric Identification
14. Filtering, Prediction and Smoothing
15. Stochastic Approximation
16. Robust Stochastic Control
• Bibliography
Index