Infinite Horizon Optimal Control

Deterministic and Stochastic Systems

  • Dean A. Carlson
  • Alain B. Haurie
  • Arie Leizarowitz

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 1-19
  3. Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 20-31
  4. Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 32-43
  5. Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 83-124
  6. Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 125-148
  7. Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 200-225
  8. Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 226-260
  9. Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 261-295
  10. Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 296-316
  11. Back Matter
    Pages 317-332

About this book

Introduction

This monograph deals with various classes of deterministic and stochastic continuous time optimal control problems that are defined over unbounded time intervals. For these problems the performance criterion is described by an improper integral and it is possible that, when evaluated at a given admissible element, this criterion is unbounded. To cope with this divergence new optimality concepts, referred to here as overtaking optimality, weakly overtaking optimality, agreeable plans, etc. , have been proposed. The motivation for studying these problems arises primarily from the economic and biological sciences where models of this type arise naturally. Indeed, any bound placed on the time hori­ zon is artificial when one considers the evolution of the state of an economy or species. The responsibility for the introduction of this interesting class of problems rests with the economists who first studied them in the modeling of capital accumulation processes. Perhaps the earliest of these was F. Ramsey [152] who, in his seminal work on the theory of saving in 1928, considered a dynamic optimization model defined on an infinite time horizon. Briefly, this problem can be described as a Lagrange problem with unbounded time interval. The advent of modern control theory, particularly the formulation of the famous Maximum Principle of Pontryagin, has had a considerable impact on the treat­ ment of these models as well as optimization theory in general.

Keywords

Infinite Horizon Kontrolltheorie Overtaking Optimality Stochastische Systeme Unbegrenzter Zeithorizont control control system control theory optimal control system

Authors and affiliations

  • Dean A. Carlson
    • 1
  • Alain B. Haurie
    • 2
  • Arie Leizarowitz
    • 3
  1. 1.Department of MathematicsUniversity of ToledoToledoUSA
  2. 2.Département d’Economie Commerciale et IndustrielleUniversité de GenèveGenèveSuisse
  3. 3.Department of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-76755-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-76757-9
  • Online ISBN 978-3-642-76755-5
  • About this book