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Necessary Properness Conditions in Periodic Control

  • Richard F. Hartl
Conference paper

Abstract

This paper deals with optimal periodic control problems and, in particular, with the question of properness. Loosely speaking this means that there is a non-trivial optimal solution which is better than the best constant solution. Two new necessary conditions for properness are presented. First, it is shown, that properness cannot occur in a one-state variable problem if the optimal solution is unique. In other words, a necessary condition for properness is that the dimension of the state space is at least two. The second result is that properness can only occur if the Hamiltonian is non-concave in the state variables.

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References

  1. Colonius F (1988) Optimal Periodic Control. Lecture Notes in Mathematics 1313. Springer Verlag. Berlin.Google Scholar
  2. Han M (1992) Optimal Periodic Control Models and their Economic Application. PhD thesis. Institute for Econometrics, O.R. and Systems Theory. Vienna University of Technology.Google Scholar
  3. Han M, Feichtinger G, Hartl R (1992) Non concavities and properness in optimal periodic control models. Working paper. Institute for Econometrics, O.R. and Systems Theory. Vienna University of Technology.Google Scholar
  4. Hartl R (1987) A simple proof of the monotonicity of the state trajectories in autonomous control problems. Journal of Economic Theory 40: 211–215.CrossRefGoogle Scholar
  5. Hartl R (1992) On the properness of one-dimensional periodic control problems. Working paper. Institute for Econometrics, O.R. and Systems Theory. Vienna University of Technology.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Richard F. Hartl
    • 1
  1. 1.Institute for Econometrics, O.R. and Systems TheoryUniversity of Techn.ViennaAustria

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