Synopses & Reviews
This text for upper-level undergraduates and graduate students explores stochastic control theory in terms of analysis, parametric optimization, and optimal stochastic control. 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, followed by an analysis of dynamical systems with inputs of stochastic processes. A simple version of the problem of optimal control of stochastic systems is discussed, along with an example of an industrial application of this theory. Subsequent discussions cover filtering and prediction theory as well as the general stochastic control problem for linear systems with quadratic criteria.
Each chapter begins with the discrete time version of a problem and progresses to a more challenging continuous time version of the same problem. Prerequisites include courses in analysis and probability theory in addition to a course in dynamical systems that covers frequency response and the state-space approach for continuous time and discrete time systems.
Synopsis
Exploration of stochastic control theory in terms of analysis, parametric optimization, and optimal stochastic control. Limited to linear systems with quadratic criteria; covers discrete time andand#160;continuous time systems. 1970 edition.
Synopsis
Exploration of stochastic control theory in terms of analysis, parametric optimization, and optimal stochastic control. Limited to linear systems with quadratic criteria; covers discrete time and continuous time systems. 1970 edition.
Table of Contents
Preface
Acknowledgments
1. Stochastic Control
and#160; 1. Introduction
and#160; 2. Theory of Feedback Control
and#160; 3. How to Characterize Disturbances
and#160; 4. Stochastic Control Theory
and#160; 5. Outline of the Contents of the Book
and#160; 6. Bibliography and Comments
2. Stochastic Processes
and#160; 1. Introduction
and#160; 2. The Concept of a Stochastic Process
and#160; 3. Some Special Stochastic Processes
and#160; 4. The Covariance Function
and#160; 5. The Concept of Spectral Density
and#160; 6. Analysis of Stochastic Processes
and#160; 7. Bibliography and Comments
3. Stochastic State Models
and#160; 1. Introduction
and#160; 2. Discrete Time Systems
and#160; 3. Solution of Stochastic Difference Equations
and#160; 4. Continuous Time Systems
and#160; 5. Stochastic Integrals
and#160; 6. Linear Stochastic Differential Equations
and#160; 7. Nonlinear Stochastic Differential Equations
and#160; 8. Stochastic Calculus--The Ito Differentiation Rule
and#160; 9. Modeling of Physical Processes by Stochastic Differential Equations
and#160; 10. Sampling a Stochastic Differential Equation
and#160; 11. Bibliography and Comments
4. Analysis of Dynamical Systems Whose Inputs are Stochastic Processes
and#160; 1. Introduction
and#160; 2. Discrete Time Systems
and#160; 3. Spectral Factorization of Discrete Time Processes
and#160; 4. Analysis of Continuous Time Systems Whose Input Signals are Stochastic Processes
and#160; 5. Spectral Factorization of Continuous Time Processes
and#160; 6. Bibliography and Comments
5. Parametric Optimization
and#160; 1. Introduction
and#160; 2. Evaluation of Loss Functions for Discrete Time Systems
and#160; 3. Evaluation of Loss Functions for Continuous Time Systems
and#160; 4. Reconstruction of State Variables for Discrete Time Systems
and#160; 5. Reconstruction of State Variables for Continuous Time Systems
and#160; 6. Bibliography and Comments
6. Minimal Variance Control Strategies
and#160; 1. Introduction
and#160; 2. A Simple Example
and#160; 3. Optimal Prediction of Discrete Time Stationary Processes
and#160; 4. Minimal Variance Control Strategies
and#160; 5. Sensitivity of the Optimal System
and#160; 6. An Industrial Application
and#160; 7. Bibliography and Comments
7. Prediction and Filtering Theory
and#160; 1. Introduction
and#160; 2. Formulation of Prediction and Estimation Problems
and#160; 3. Preliminaries
and#160; 4. State Estimation for Discrete Time Systems
and#160; 5. Duality
and#160; 6. State Estimation for Continuous Time Processes
and#160; 7. Bibliography and Comments
8. Linear Stochastic Control Theory
and#160; 1. Introduction
and#160; 2. Formulation
and#160; 3. Preliminaries
and#160; 4. Complete State Information
and#160; 5. Incomplete State Information 1
and#160; 6. Incomplete State Information 2
and#160; 7. Continuous Time Problems
and#160; 8. Bibliography and Comments
Index