Adaptive Markov Control Processes

  • O. Hernández-Lerma

Part of the Applied Mathematical Sciences book series (AMS, volume 79)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. O. Hernández-Lerma
    Pages 1-16
  3. O. Hernández-Lerma
    Pages 17-50
  4. O. Hernández-Lerma
    Pages 51-82
  5. O. Hernández-Lerma
    Pages 83-97
  6. O. Hernández-Lerma
    Pages 98-106
  7. O. Hernández-Lerma
    Pages 107-121
  8. Back Matter
    Pages 122-149

About this book

Introduction

This book is concerned with a class of discrete-time stochastic control processes known as controlled Markov processes (CMP's), also known as Markov decision processes or Markov dynamic programs. Starting in the mid-1950swith Richard Bellman, many contributions to CMP's have been made, and applications to engineering, statistics and operations research, among other areas, have also been developed. The purpose of this book is to present some recent developments on the theory of adaptive CMP's, i. e. , CMP's that depend on unknown parameters. Thus at each decision time, the controller or decision-maker must estimate the true parameter values, and then adapt the control actions to the estimated values. We do not intend to describe all aspects of stochastic adaptive control; rather, the selection of material reflects our own research interests. The prerequisite for this book is a knowledgeof real analysis and prob­ ability theory at the level of, say, Ash (1972) or Royden (1968), but no previous knowledge of control or decision processes is required. The pre­ sentation, on the other hand, is meant to beself-contained,in the sensethat whenever a result from analysisor probability is used, it is usually stated in full and references are supplied for further discussion, if necessary. Several appendices are provided for this purpose. The material is divided into six chapters. Chapter 1 contains the basic definitions about the stochastic control problems we are interested in; a brief description of some applications is also provided.

Keywords

Estimator Markov decision process Markov process Observable ergodicity statistics

Authors and affiliations

  • O. Hernández-Lerma
    • 1
  1. 1.Departamento de MatemáticasCentro de Investigación del IPNMéxico, D.F.México

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-8714-3
  • Copyright Information Springer-Verlag New York Inc. 1989
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6454-5
  • Online ISBN 978-1-4419-8714-3
  • Series Print ISSN 0066-5452
  • About this book