Continuous average control of piecewise deterministic Markov processes Oswaldo Luiz do Valle Costa, Francois Dufour

Format:

Book

Author/Creator:

Costa, Oswaldo Luiz do Valle

Contributor:

Dufour, François (Mathematician)

Series:

SpringerBriefs in mathematics

SpringerBriefs in mathematics 2191-8198

Language:

English

Subjects (All):

Control theory--Mathematical models.

Control theory.

Markov processes.

Markov Chains.

Mathematics.

Probability Theory and Stochastic Processes.

Continuous Optimization.

Systems Theory, Control.

Operations Research, Management Science.

Complex Systems.

Medical Subjects:

Markov Chains.

Local Subjects:

Mathematics.

Probability Theory and Stochastic Processes.

Continuous Optimization.

Systems Theory, Control.

Operations Research, Management Science.

Complex Systems.

Physical Description:

1 online resource

Place of Publication:

New York, NY Springer ©2013

Language Note:

English

System Details:

PDF

text file

Summary:

"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."--Publisher's website

Contents:

Introduction Average Continuous Control of PDMPs Optimality Equation for the Average Control of PDMPs The Vanishing Discount Approach for PDMPs The Policy Iteration Algorithm for PDMPs Examples

Machine generated contents note: 1. Introduction

1.1. Preliminaries

1.2. Overview of the Chapters

1.3. General Comments and Historical Remarks

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

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: Lα, Lα, Gα, Hα

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

4. Vanishing Discount Approach for PDMPs

4.1. Outline of the Chapter

4.2. Optimality Equation for the Discounted Case

4.3. Vanishing Discount Approach: First Case

4.4. 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

5. Policy Iteration Algorithm for PDMPs

5.1. Outline of the Chapter

5.2. Assumptions and a Pseudo-Poisson Equation

5.3. Policy Iteration Algorithm

5.3.1. Convergence of the PIA

5.3.2. Optimality of the PIA

6. Examples

6.1. Outline of the Chapter

6.2. Capacity Expansion Problem

6.3. First Example

6.3.1. Verification of the Assumptions in Sect. 4.3

6.3.2. Numerical Example

6.4. Second Example

6.4.1. Verification of the Assumptions in Sect. 4.3

6.4.2. Numerical Example

6.5. Third Example

Notes:

Includes bibliographical references and index

Print version record

Other Format:

Print version Costa, Oswaldo Luiz do Valle. Continuous average control of piecewise deterministic Markov processes

ISBN:

9781461469834

146146983X

OCLC:

840605078

Access Restriction:

Restricted for use by site license