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© 2018

Finite Approximations in Discrete-Time Stochastic Control

Quantized Models and Asymptotic Optimality

Benefits

  • Demonstrates how quantization can be used to systematically optimize decentralized stochastic control problems

  • Explores network control applications

  • Provides a framework for comparing approximation models

Book

Part of the Systems & Control: Foundations & Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Naci Saldi, Tamás Linder, Serdar Yüksel
    Pages 1-11
  3. Finite Model Approximations in Stochastic Control

    1. Front Matter
      Pages 13-13
    2. Naci Saldi, Tamás Linder, Serdar Yüksel
      Pages 15-21
    3. Naci Saldi, Tamás Linder, Serdar Yüksel
      Pages 23-48
    4. Naci Saldi, Tamás Linder, Serdar Yüksel
      Pages 49-97
    5. Naci Saldi, Tamás Linder, Serdar Yüksel
      Pages 99-123
    6. Naci Saldi, Tamás Linder, Serdar Yüksel
      Pages 125-149
  4. Finite Model Approximations in Decentralized Stochastic Control

    1. Front Matter
      Pages 151-151
    2. Naci Saldi, Tamás Linder, Serdar Yüksel
      Pages 153-157
    3. Naci Saldi, Tamás Linder, Serdar Yüksel
      Pages 159-175
    4. Naci Saldi, Tamás Linder, Serdar Yüksel
      Pages 177-188
  5. Back Matter
    Pages 189-198

About this book

Introduction

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.

Keywords

stochastic control decentralized stochastic control quantization numerical approximation finite state approximations Markov decision processes asymptotic optimality

Authors and affiliations

  1. 1.Department of Natural and Mathematical SciencesOzyegin UniversityIstanbulTurkey
  2. 2.Department of Mathematics and StatisticsQueen’s UniversityKingstonCanada
  3. 3.Department of Mathematics & StatisticsQueen’s UniversityKingstonCanada

Bibliographic information

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)​