Åström K. Introduction to stochastic control theory

Academic Press, 1970. — 299 p.The object of this book is to present stochastic control theory — analysis, parametric optimization and optimal stochastic control. The treatment is limited to linear systems with quadratic criteria. It covers discrete time as well as continuous time systems.
The first three chapters provide motivation and background material on stochastic processes. Chapter 4 is devoted to analysis of dynamical systems whose inputs are stochastic processes. A simple version of the problem of optimal control of stochastic systems is discussed in Chapter 6; this chapter also contains an example of an industrial application of this theory. Filtering and prediction theory are covered in Chapter 7, and the general stochastic control problem for linear systems with quadratic criteria is treated in Chapter 8.
In each chapter we shall first discuss the discrete time version of a problem. We shall then turn to the continuous time version of the same problem. The continuous time problems are more difficult both analytically and conceptually. Chapter 6 is an exception because it deals only with discrete time systems.Stochastic Control.Theory of Feedback Control.
How to Characterize Disturbances.
Stochastic Control Theory.
Outline of the Contents of the Book.
Bibliography and Comments.
Stochastic Processes.The Concept of a Stochastic Process.
Some Special Stochastic Processes.
The Covariance Function.
The Concept of Spectral Density.
Analysis of Stochastic Processes.
Bibliography and Comments.
Stochastic State Models.Discrete Time Systems.
Solution of Stochastic Difference Equations.
Continuous Time Systems.
Stochastic Integrals.
Linear Stochastic Differential Equations.
Nonlinear Stochastic Differential Equations.
Stochastic Calculus—The Ito Differentiation Rule.
Modeling of Physical Processes by Stochastic Differential Equations.
Sampling a Stochastic Differential Equation.
Bibliography and Comments.
Analysis of Dynamical Systems Whose Inputs Are Stochastic Processes.Discrete Time Systems.
Spectral Factorization of Discrete Time Processes.
Analysis of Continuous Time Systems Whose Input Signals Are Stochastic Processes.
Spectral Factorization of Continuous Time Processes.
Bibliography and Comments.
Parametric Optimization.Evaluation of Loss Functions for Discrete Time Systems.
Evaluation of Loss Functions for Continuous Time Systems.
Reconstruction of State Variables for Discrete Time Systems.
Reconstruction of State Variables for Continuous Time Systems.
Bibliography and Comments.
Minimal Variance Control Strategies.A Simple Example.
Optimal Prediction of Discrete Time Stationary Processes.
Minimal Variance Control Strategies.
Sensitivity of the Optimal System.
An Industrial Application.
Bibliography and Comments.
Prediction And Filtering Theory.Formulation of Prediction and Estimation Problems.
Preliminaries.
State Estimation for Discrete Time Systems.
Duality.
State Estimation for Continuous Time Processes.
Bibliography and Comments.
Linear Stochastic Control Theory.Formulation.
Preliminaries.
Complete State Information.
Incomplete State Information 1.
Incomplete State Information 2.
Continuous Time Problems.
Bibliography and Comments.