1st Edition

Linear Stochastic Control Systems



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ISBN 9780849380754
Published July 12, 1995 by CRC Press
400 Pages

USD $280.00

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Book Description

Linear Stochastic Control Systems presents a thorough description of the mathematical theory and fundamental principles of linear stochastic control systems. Both continuous-time and discrete-time systems are thoroughly covered.
Reviews of the modern probability and random processes theories and the Itô stochastic differential equations are provided. Discrete-time stochastic systems theory, optimal estimation and Kalman filtering, and optimal stochastic control theory are studied in detail. A modern treatment of these same topics for continuous-time stochastic control systems is included. The text is written in an easy-to-understand style, and the reader needs only to have a background of elementary real analysis and linear deterministic systems theory to comprehend the subject matter.
This graduate textbook is also suitable for self-study, professional training, and as a handy research reference. Linear Stochastic Control Systems is self-contained and provides a step-by-step development of the theory, with many illustrative examples, exercises, and engineering applications.

Table of Contents

Preface
Introduction
From Deterministic to Stochastic Linear Control Systems
Text Organization and Reading Suggestion
MATHEMATICAL PRELIMINARIES
Probability and Random Processes
Probability, Measure, and Integration
Convergence of Random Sequences
Random Vectors and Conditional Expectations
Second Order Processes and Calculus in Mean Square
Exercises
References
Itô Integrals and Stochastic Differential Equations
Markov Processes
Orthogonal Increments Processes and the Wiener-Lévy Process
Itô Integrals and Stochastic Differential Equations
Exercises
References
LINEAR STOCHASTIC CONTROL SYSTEMS: THE DISCRETE-TIME CASE
Analysis of Discrete-Time Linear Stochastic Control Systems
Analysis of Discrete-Time Causal LTI Systems
Analysis of Causal LTI Stochastic Control Systems
Analysis of the "State" Description of Controlled Markov Chains
State Space Systems and ARMA Models
Mathematical Modeling and Applications
Exercises
References
Optimal Estimation for Discrete-Time Linear Stochastic Systems
Optimal State Estimation
Recursive Optimal Estimation and Kalman Filtering
Modified Kalman Filtering Algorithms
Exercises
References
Optimal Control of Discrete-Time Linear Stochastic Systems
Introduction
Dynamic Programming and LQC Control Problems
LQC Optimal Control Problems
Adaptive Stochastic Control
Exercises
References
LINEAR STOCHASTIC CONTROL SYSTEMS: THE CONTINUOUS-TIME CASE
Continuous-Time Linear Stochastic Control Systems
Analysis of Continuous-Time Causal LTI Systems
Further Discussion of Markov Processes
Dynamic Programming and LQ Control Problems
Exercises
References
Optimal Control of Continuous-Time Linear Stochastic Systems
The Continuous-Time LQ Stochastic Control Problem
Stochastic Dynamic Programming
Innovation Processes and the Kalman-Bucy Filter
Optimal Prediction and Smoothing
The Separation Principle
Exercises
References
Stability Analysis of Stochastic Differential Equations
Stability of Deterministic Systems
Stability of Stochastic Systems
Stability of Moments
Exercises
References
Appendix
Fundamental Real and Functional Analysis
Fundamental Matrix Theory and Vector Calculations
Martingales
References
Index

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Author(s)

Biography

Chen\, Goong; Chen\, Guanrong; Hsu\, Shih-Hsun