Introduction to Stochastic Control Theory

Preface Acknowledgments 1. Stochastic Control 1. Introduction 2. Theory of Feedback Control 3. How to Characterize Disturbances 4. Stochastic Control Theory 5. Outline of the Contents of the Book 6. Bibliography and Comments 2. Stochastic Processes 1. Introduction 2. The Concept of a Stochastic Process 3. Some Special Stochastic Processes 4. The Covariance Function 5. The Concept of Spectral Density 6. Analysis of Stochastic Processes 7. Bibliography and Comments 3. Stochastic State Models 1. Introduction 2. Discrete Time Systems 3. Solution of Stochastic Difference Equations 4. Continuous Time Systems 5. Stochastic Integrals 6. Linear Stochastic Differential Equations 7. Nonlinear Stochastic Differential Equations 8. Stochastic Calculus--The Ito Differentiation Rule 9. Modeling of Physical Processes by Stochastic Differential Equations 10. Sampling a Stochastic Differential Equation 11. Bibliography and Comments 4. Analysis of Dynamical Systems Whose Inputs are Stochastic Processes 1. Introduction 2. Discrete Time Systems 3. Spectral Factorization of Discrete Time Processes 4. Analysis of Continuous Time Systems Whose Input Signals are Stochastic Processes 5. Spectral Factorization of Continuous Time Processes 6. Bibliography and Comments 5. Parametric Optimization 1. Introduction 2. Evaluation of Loss Functions for Discrete Time Systems 3. Evaluation of Loss Functions for Continuous Time Systems 4. Reconstruction of State Variables for Discrete Time Systems 5. Reconstruction of State Variables for Continuous Time Systems 6. Bibliography and Comments 6. Minimal Variance Control Strategies 1. Introduction 2. A Simple Example 3. Optimal Prediction of Discrete Time Stationary Processes 4. Minimal Variance Control Strategies 5. Sensitivity of the Optimal System 6. An Industrial Application 7. Bibliography and Comments 7. Prediction and Filtering Theory 1. Introduction 2. Formulation of Prediction and Estimation Problems 3. Preliminaries 4. State Estimation for Discrete Time Systems 5. Duality 6. State Estimation for Continuous Time Processes 7. Bibliography and Comments 8. Linear Stochastic Control Theory 1. Introduction 2. Formulation 3. Preliminaries 4. Complete State Information 5. Incomplete State Information 1 6. Incomplete State Information 2 7. Continuous Time Problems 8. Bibliography and Comments Index