Skip to main content
SpringerLink
Log in

Continuous Average Control of Piecewise Deterministic Markov Processes

  • Book
  • © 2013

Overview

Authors:
  1. Oswaldo Luiz do Valle Costa

    1. , Telecommunications and Control Eng, University of São Paulo, São Paulo, Brazil

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Francois Dufour

    1. , Institut de Mathématiques de Bordeaux, Institut Polytechnique de Bordeaux, Talence cedex, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • 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

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 34.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 49.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (6 chapters)

  1. Front Matter

    Pages i-xii
    Download chapter PDF

  2. Introduction

    • Oswaldo Luiz do Valle Costa, François Dufour
    Pages 1-5

  3. Average Continuous Control of PDMPs

    • Oswaldo Luiz do Valle Costa, François Dufour
    Pages 7-22

  4. Optimality Equation for the Average Control of PDMPs

    • Oswaldo Luiz do Valle Costa, François Dufour
    Pages 23-46

  5. The Vanishing Discount Approach for PDMPs

    • Oswaldo Luiz do Valle Costa, François Dufour
    Pages 47-77

  6. The Policy Iteration Algorithm for PDMPs

    • Oswaldo Luiz do Valle Costa, François Dufour
    Pages 79-91

  7. Examples

    • Oswaldo Luiz do Valle Costa, François Dufour
    Pages 93-110

  8. Back Matter

    Pages 111-116
    Download chapter PDF
Back to top

Keywords

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)

Authors and Affiliations

  • , Telecommunications and Control Eng, University of São Paulo, São Paulo, Brazil

    Oswaldo Luiz do Valle Costa

  • , Institut de Mathématiques de Bordeaux, Institut Polytechnique de Bordeaux, Talence cedex, France

    Francois Dufour

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation