Finite Approximations in Discrete-Time Stochastic Control : Quantized Models and Asymptotic Optimality / by Naci Saldi, Tamás Linder, Serdar Yüksel.

Format:

Book

Author/Creator:

Saldi, Naci, author.

Linder, Tamás, author.

Yüksel, Serdar, author.

Contributor:

SpringerLink (Online service)

Series:

Mathematics and Statistics (Springer-11649)

Systems & control 2324-9749

Systems & Control: Foundations & Applications, 2324-9749

Language:

English

Subjects (All):

Calculus of variations.

System theory.

Automatic control.

Probabilities.

Approximation theory.

Calculus of Variations and Optimal Control; Optimization.

Systems Theory, Control.

Control and Systems Theory.

Probability Theory and Stochastic Processes.

Approximations and Expansions.

Local Subjects:

Calculus of Variations and Optimal Control; Optimization.

Systems Theory, Control.

Control and Systems Theory.

Probability Theory and Stochastic Processes.

Approximations and Expansions.

Physical Description:

1 online resource (VII, 198 pages) : 6 illustrations.

Edition:

First edition 2018.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.

System Details:

text file PDF

Summary:

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.

Contents:

Introduction and Summary

Part I: Finite Model Approximations in Stochastic Control

Prelude to Part I

Finite Action Approximation of Markov Decision Processes

Finite-State Approximation of Markov Decision Processes

Approximations for Partially Observed Markov Decision Processes

Approximations for Constrained Markov Decision Problems

Part II: Finite Model Approximations in Decentralized Stochastic Control

Prelude to Part II

Finite Model Approximations in Decentralized Stochastic Control

Asymptotic Optimality of Finite Models for Specific Systems

Index

References.

Other Format:

Printed edition:

ISBN:

978-3-319-79033-6

9783319790336

Access Restriction:

Restricted for use by site license.