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Infinite Horizon Optimal Control

Deterministic and Stochastic Systems

  • Book
  • © 1991

Overview

Authors:
  1. Dean A. Carlson

    1. Department of Mathematics, University of Toledo, Toledo, USA

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  2. Alain B. Haurie

    1. Département d’Economie Commerciale et Industrielle, Université de Genève, Genève, Suisse

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  3. Arie Leizarowitz

    1. Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Dynamical Systems with Unbounded Time Interval in Engineering, Ecology and Economics

    • Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 1-19

  3. Necessary Conditions and Sufficient Conditions for Optimality

    • Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 20-31

  4. Asymptotic Stability and the Turnpike Property in Some Simple Control Problems

    • Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 32-43

  5. Global Asymptotic Stability and Existence of Optimal Trajectories for Infinite Horizon Autonomous Convex Systems

    • Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 44-82

  6. The Reduction to Finite Rewards

    • Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 83-124

  7. Asymptotic Stability with a Discounted Criterion; Global and Local Analysis

    • Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 125-148

  8. Turnpike Properties and Existence of Overtaking Optimal Solutions for Classes of Nonautonomous Nonconvex Control Problems

    • Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 149-199

  9. Control of Systems with Integrodifferential Equations

    • Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 200-225

  10. Extensions to Distributed Parameter Systems

    • Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 226-260

  11. Stochastic Control with the Overtaking Criterion

    • Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 261-295

  12. Maximum Principle and Turnpike Properties for Systems with Random Modal Jumps

    • Dean A. Carlson, Alain B. Haurie, Arie Leizarowitz
    Pages 296-316

  13. Back Matter

    Pages 317-332
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Toledo, Toledo, USA

    Dean A. Carlson

  • Département d’Economie Commerciale et Industrielle, Université de Genève, Genève, Suisse

    Alain B. Haurie

  • Department of Mathematics, Technion-Israel Institute of Technology, Haifa, Israel

    Arie Leizarowitz

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