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Tables of Contents for Linear Stochastic Control Systems
Chapter/Section Title
Page #
Page Count
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
It( Integrals and Stochastic Differential Equations
Markov Processes
Orthogonal Increments Processes and the Wiener-LTvy Process
It( 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