Systems & Control: Foundations & Applications

Finite Approximations in Discrete-Time Stochastic Control

Quantized Models and Asymptotic Optimality

Authors: Saldi, Naci, Linder, Tamas, Yuksel, Serdar

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  • Demonstrates how quantization can be used to systematically optimize decentralized stochastic control problems
  • Explores network control applications
  • Provides a framework for comparing approximation models
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  • ISBN 978-3-319-79033-6
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Hardcover $109.99
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  • ISBN 978-3-319-79032-9
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Softcover $79.99
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  • ISBN 978-3-030-07710-5
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About this book

In a unified form, this monograph presents fundamental results on the approximation of centralized and decentralized stochastic control problems, with uncountable state, measurement, and action spaces. It demonstrates how quantization provides a system-independent and constructive method for the reduction of a system with Borel spaces to one with finite state, measurement, and action spaces. In addition to this constructive view, the book considers both the information transmission approach for discretization of actions, and the computational approach for discretization of states and actions. Part I of the text discusses Markov decision processes and their finite-state or finite-action approximations, while Part II builds from there to finite approximations in decentralized stochastic control problems. 
This volume is perfect for researchers and graduate students interested in stochastic controls. With the tools presented, readers will be able to establish the convergence of approximation models to original models and the methods are general enough that researchers can build corresponding approximation results, typically with no additional assumptions.

Reviews

“This book is an interesting and complete treatise on finite approximations of different kinds of discrete-time stochastic control problems. It is based on several recent research results on the topic presented which have been published in various papers written by the authors.” (Raúl Montes-de-Oca, Mathematical Reviews, March, 2019)​

Table of contents (9 chapters)

Table of contents (9 chapters)
  • Introduction and Summary

    Pages 1-11

    Saldi, Naci (et al.)

  • Prelude to Part I

    Pages 15-21

    Saldi, Naci (et al.)

  • Finite-Action Approximation of Markov Decision Processes

    Pages 23-48

    Saldi, Naci (et al.)

  • Finite-State Approximation of Markov Decision Processes

    Pages 49-97

    Saldi, Naci (et al.)

  • Approximations for Partially Observed Markov Decision Processes

    Pages 99-123

    Saldi, Naci (et al.)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-3-319-79033-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-319-79032-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
Softcover $79.99
price for USA in USD
  • ISBN 978-3-030-07710-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Finite Approximations in Discrete-Time Stochastic Control
Book Subtitle
Quantized Models and Asymptotic Optimality
Authors
Series Title
Systems & Control: Foundations & Applications
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-79033-6
DOI
10.1007/978-3-319-79033-6
Hardcover ISBN
978-3-319-79032-9
Softcover ISBN
978-3-030-07710-5
Series ISSN
2324-9749
Edition Number
1
Number of Pages
VII, 198
Number of Illustrations
6 b/w illustrations
Topics