Optimal Control with Multiple Criteria and Time Lags: Some Economic Applications

  • Mohamed El-Hodiri
  • Fred S. Van Vleck
Conference paper
Part of the Operations Research Proceedings book series (ORP, volume 1988)


Consider a system where the motion is given by
$$ x\left( t \right)\, = \,f\left( {t,\;x\left( {t - {z_{r}}} \right), \ldots ,\;x\left( {t - {z_{1}}} \right),\;x\left( t \right),\;u\left( {t - {\alpha _{3}}} \right)\;,\; \ldots ,u\left( {t - {\alpha _{1}}} \right),\;u\left( t \right)} \right) = f\left( {t,x,v} \right) $$
where x(t) ∈ En and u(t) ∈ Em for any given t, where X represents all state variables-current and delayed- and where U represents all control variables.




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  1. 1.
    Ragner Frisch: The mathematical structure of a decision model: The Oslo submodel. Metroeconomica, vol. 7, 1955.Google Scholar
  2. 2.
    A. Halanay: Optimal control for systems with time lags. SIAM Journal on Control, vol. 6, 1966.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Mohamed El-Hodiri
    • 1
  • Fred S. Van Vleck
    • 2
  1. 1.Dept of EconomicsUniversity of KansasUSA
  2. 2.Dept of MathematicsUniv. of KansasUSA

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