SpringerBriefs in Mathematics

Continuous Average Control of Piecewise Deterministic Markov Processes

Authors: Costa, Oswaldo Luiz do Valle, Dufour, Francois

  • ​Uses the special features of the Piecewise Deterministic Markov Processes (PDMPs)
  • Traces a parallel with the general theory for discrete-time Markov Decision Processes
  • ​Uses the powerful tools developed in the discrete-time framework
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About this book

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.

 

Reviews

From the reviews:

“This book is a successful attempt to present a recent progress in some control problems for the class of Piecewise Deterministic Markov Processes (PDMP). … The book is addressed to readers who are well prepared. … The detailed description of problems, results, proofs and numerical illustrations makes the book a valuable source for many people working in stochastic control.” (Jordan M. Stoyanov, zbMATH, Vol. 1272, 2013)

Table of contents (6 chapters)

  • Introduction

    Costa, Oswaldo Luiz (et al.)

    Pages 1-5

  • Average Continuous Control of PDMPs

    Costa, Oswaldo Luiz (et al.)

    Pages 7-22

  • Optimality Equation for the Average Control of PDMPs

    Costa, Oswaldo Luiz (et al.)

    Pages 23-46

  • The Vanishing Discount Approach for PDMPs

    Costa, Oswaldo Luiz (et al.)

    Pages 47-77

  • The Policy Iteration Algorithm for PDMPs

    Costa, Oswaldo Luiz (et al.)

    Pages 79-91

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-1-4614-6983-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-1-4614-6982-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Continuous Average Control of Piecewise Deterministic Markov Processes
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Oswaldo Luiz do Valle Costa, François Dufour
eBook ISBN
978-1-4614-6983-4
DOI
10.1007/978-1-4614-6983-4
Softcover ISBN
978-1-4614-6982-7
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XII, 116
Number of Illustrations and Tables
2 b/w illustrations
Topics