无穷区间受控马氏切换扩散系统先进最优准则

Preface

Notation

1 Introduction

1.1 Motivational Examples

1.2 Related Literature

1.3 Outline

2 Control Models and Ergodicity

2.1 The Controlled System

2.2 Control Policies and Extended Generator

2.3 Positive Recurrence and Ergodicity

2.4 Conclusions

3 Basic Optimality Criteria

3.1 Discounted Reward Criterion

3.2 An LQ Example： Discounted Case

3.3 A Pollution Accumulation Example

3.4 Ergodic Reward Criterion

3.5 An LQ System Example： Average Case

3.6 A Pollution Accumulation Example

3.7 Conclusions

4 Bias Optimality

4.1 Preliminaries

4.2 Existence of Bias Optimal Policies

4.3 Overtaking Optimality

4.4 Asymptotic Rate of Average Optimal Policies

4.5 A Pollution Accumulation Example

4.6 Conclusions

5 Sensitive-Discount Optimality

5.1 m-Discount Optimality

5.2 Poisson Equation and Average Reward HJB Equation

5.3 Laurent Series

5.4 Existence and Characterizations of m-Discount Optimal Policies

5.5 Special Cases： m —— -1 and m = 0

5.6 Blackwell Optimality

5.7 A Pollution Accumulation Example

5.8 Conclusions

6 Concluding Remarks

References

A Technical Complements

Index

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