Continuous Average Control Of Piecewise Deterministic Markov Processes 2013th Edition Oswaldo Luiz Do Valle Costa by Oswaldo Luiz Do Valle Costa, Francois Dufour 9781461469827, 1461469821 instant download after payment.

The intent of this book is to present recent results in the control theory for the long run average continuous control problem of piecewise deterministic Markov processes (PDMPs). The book focuses mainly on the long run average cost criteria and extends to the PDMPs some well-known techniques related to discrete-time and continuous-time Markov decision processes, including the so-called ``average inequality approach'', ``vanishing discount technique'' and ``policy iteration algorithm''. We believe that what is unique about our approach is that, by using the special features of the PDMPs, we trace a parallel with the general theory for discrete-time Markov Decision Processes rather than the continuous-time case. The two main reasons for doing that is to use the powerful tools developed in the discrete-time framework and to avoid working with the infinitesimal generator associated to a PDMP, which in most cases has its domain of definition difficult to be characterized. Although the book is mainly intended to be a theoretically oriented text, it also contains some motivational examples. The book is targeted primarily for advanced students and practitioners of control theory. The book will be a valuable source for experts in the field of Markov decision processes. Moreover, the book should be suitable for certain advanced courses or seminars. As background, one needs an acquaintance with the theory of Markov decision processes and some knowledge of stochastic processes and modern analysis.
Table of Contents
Cover
Continuous Average Control of Piecewise Deterministic Markov Processes
ISBN 9781461469827 ISBN 9781461469834
Preface
Contents
Notation and Conventions
Chapter 1 Introduction
1.1 Preliminaries
1.2 Overview of the Chapters
1.3 General Comments and Historical Remarks
Chapter 2 Average Continuous Control of PDMPs
2.1 Outline of the Chapter
2.2 Notation, Assumptions, and Problem Formulation
2.3 Discrete-Time Markov Control Problem
2.3.1 Discrete-Time Ordinary and Relaxed Controls
2.3.2 Discrete-Time Operators and Measurability Properties
2.4 Proofs of the Results of Section 2.3
Chapter 3 Optimality Equation for the Average Control of PDMPs
3.1 Outline of the Chapter
3.2 Discrete-Time Optimality Equation for the Average Control
3.3 Convergence and Continuity Properties of the Operators:
3.4 Existence of an Ordinary Optimal Feedback Control
3.5 Proof of Auxiliary Results
3.5.1 Proofs of the Results of Sect. 3.2
3.5.2 Proofs of the Results of Sect. 3.3
3.5.3 Proofs of the Results of Sect. 3.4
Chapter 4 The Vanishing Discount Approach for PDMPs
4.1 Outline of the Chapter
4.2 Optimality Equation for the Discounted Case
4.3 The Vanishing Discount Approach: First Case
4.4 The Vanishing Discount Approach: Second Case
4.4.1 Assumptions on the Parameters of the PDMP
4.4.2 Main Results
4.5 Proof of the Results of Section 4.4.2
4.5.1 Proof of Theorem 4.20
4.5.2 Proof of Theorem 4.21
4.5.3 Existence of an Ordinary Feedback Measurable Selector
Chapter 5 The Policy Iteration Algorithm for PDMPs
5.1 Outline of the Chapter
5.2 Assumptions and a Pseudo-Poisson Equation
5.3 The Policy Iteration Algorithm
5.3.1 Convergence of the PIA
5.3.2 Optimality of the PIA
Chapter 6 Examples
6.1 Outline of the Chapter
6.2 The Capacity Expansion Problem
6.3 First Example 6.3.1 Verificatio of the Assumptions in Sect. 4.3
6.3.2 Numerical Example
6.4 Second Example 6.4.1 Verificatio of the Assumptions in Sect. 4.3
6.4.2 Numerical Example
6.5 Third Example