Optimization of Stochastic Systems

Name: Optimization of Stochastic Systems | Topics in Discrete-Time Systems
Brand: Academic Press
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Topics in Discrete-Time Systems

Masanao Aoki(Author)

Richard Bellman(Editor)

Academic Press

Published on 3. June 2016

372 pages

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978-1-4832-2405-3 (ISBN)

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Front Cover
Optimization of Stochastic Systems: Topics in Discrete-Time Systems
Copyright Page
Table of Contents
Dedication
Preface
Chapter I. Introduction
1. Introduction
2. Preliminary Examples
Chapter II. Optimal Bayesian Control of General Stochastic Dynamic Systems
1. Formulation of Optimal Control Problems
2. Example. Linear Control Systems with Independent Parameter Variations
3. Sufficient Statistics
4. Discussions
Appendix A. Minimization of a Quadratic Form
Appendix B. Use of Pseudoinverse in Minimizing a Quadratic Form
Appendix C. Calculation of Sufficient Statistics
Appendix D. Matrix Identities
Chapter III. Adaptive Control Systems and Optimal Bayesian Control Policies
1. General Problem Statement (Scope of the Discussions)
2. Systems with Unknown Noise Characteristics
3. Systems with Unknown Plant Parameters
4. Systems with Unknown Plant Parameters and Noise Characteristics
5. Sufficient Statistics
6. Method Based on Computing Joint Probability Density
7. Discussions
Chapter IV. Optimal Bayesian Control of Partially Observed Markovian Systems
1. Introduction
2. Markov Properties
3. Optimal Control Policies
4. Derivation of Conditional Probability Densities
5. Examples
Chapter V. Problem of Estimation
1. Least-Squares Estimation
2. Maximum Likelihood Estimation
3. Optimal Bayesian Estimation
Appendix. Completion of Squares
Chapter VI. Convergence Questions in Bayesian Optimization Problems
1. Introduction
2. Convergence Questions: A Simple Case
3. Martingales
4. Convergence Questions: General Case
5. Stochastic Controllability and Observability
Chapter VII. Approximations
1. Approximately Optimal Control Policies for Adaptive Systems
2. Approximation with Open-Loop Feedback Control Policies
3. Sensitivity and Error Analysis of Kaiman Filters
4. Estimation of State Vectors by a Minimal-Order Observer
5. Suboptimal Linear Estimation by State Vector Partition Method: Theory
6. Suboptimal Estimation by State Vector Partition: An Example
Appendix A. Derivation of the Recursion Formula for Open-Loop Feedback Control Policies (Section 2)
Appendix B. Derivation of the Constraint Matrix Equations (Section 4)
Appendix C. Computation of ?G(i) (Section 6)
Chapter VIII. Stochastic Stability
1. Introduction
2. Stochastic Lyapunov Functions as Semimartingales
3. Examples
Appendix. Semimartingale Inequality
Chapter IX. Miscellany
1. Probability as a Performance Criterion
2. Min-Max Control Policies
3. Extensions and Future Problems
Appendix I: Some Useful Definitions, Facts, and Theorems from Probability Theory
Appendix II: Pseudoinverse
Appendix III: Multidimensional Normal Distributions
Appendix IV: Sufficient Statistics
Bibliography
REFERENCES
LIST OF SYMBOLS
Author Index
Subject Index

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Optimization of Stochastic Systems

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