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Numerical Solution of Optimal Control Problems with Constant Control Delays

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  • Ulrich Brandt-Pollmann
  • Ralph Winkler

    ()

  • Sebastian Sager
  • Ulf Moslener
  • Johannes Schlöder

Abstract

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a state-of-the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Article provided by Society for Computational Economics in its journal Computational Economics.

Volume (Year): 31 (2008)
Issue (Month): 2 (March)
Pages: 181-206

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Handle: RePEc:kap:compec:v:31:y:2008:i:2:p:181-206

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Web page: http://www.springerlink.com/link.asp?id=100248
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Keywords: Delayed differential equations; Delayed optimal control; Numerical optimization; C63; C61;

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References

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  1. Collard, Fabrice & Licandro, Omar & Puch, Luis, 2005. "The Short-Run Dynamics of Optimal Growth Models with Delays," CEPR Discussion Papers 5414, C.E.P.R. Discussion Papers.
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  4. Peeters, Marga, 1996. "Investment gestation lags: The difference between time-to-build and delivery lags," MPRA Paper 28549, University Library of Munich, Germany.
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  11. Winkler, Ralph & Brandt-Pollmann, Ulrich & Moslener, Ulf & Schlöder, Johannes, 2005. "On the Transition from Instantaneous to Time-Lagged Capital Accumilation: The Case of Leontief Type Production Functions," ZEW Discussion Papers 05-30, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  12. de la Croix, David & Licandro, Omar, 1997. "Life expectancy and endogenous growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1997029, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
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Citations

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Cited by:
  1. Edward J. Balistreri & Russell H. Hillberry & Thomas F. Rutherford, 2008. "Structural Estimation and Solution of International Trade Models with Heterogeneous Firms," CER-ETH Economics working paper series 08/89, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  2. Cyril Bourgeois & Pierre-Alain Jayet, 2010. "Revisited water-oriented relationships between a set of farmers and an aquifer: accounting for lag effect," Working Papers 2010/06, INRA, Economie Publique.
  3. Ralph Winkler, 2008. "Optimal control of pollutants with delayed stock accumulation," CER-ETH Economics working paper series 08/91, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.

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