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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