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Numerical solution of optimal control problems with constant control delays

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Author Info
Ulrich Brandt-Pollmann (Interdisciplinary Center for Scientific Computing, University of Heidelberg, Germany)
Ralph Winkler () (Center of Economic Research (CER-ETH) at ETH Zürich)
Sebastian Sager (Interdisciplinary Center for Scientific Computing, University of Heidelberg, Germany)
Ulf Moslener (Centre for European Economic Research (ZEW), Mannheim, Germany)
Johannes P. Schlöder (Interdisciplinary Center for Scientific Computing, University of Heidelberg, Germany)

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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.

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Publisher Info
Paper provided by CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich in its series CER-ETH Economics working paper series with number 06/59.

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Length: 26 pages
Date of creation: Oct 2006
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Handle: RePEc:eth:wpswif:06-59

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Related research
Keywords: delayed differential equations; delayed optimal control; numerical optimization; time-to-build;

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Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis

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  1. Hans Gersbach & Markus Müller, 2006. "Elections, Contracts and Markets," CER-ETH Economics working paper series 06/56, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich. [Downloadable!]
    Other versions:
  2. Boyer, Marcel, 1978. "A Habit Forming Optimal Growth Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(3), pages 585-609, October. [Downloadable!] (restricted)
    Other versions:
  3. Christopher D. Carroll & Jody Overland & David N. Weil, 2000. "Saving and Growth with Habit Formation," American Economic Review, American Economic Association, vol. 90(3), pages 341-355, June. [Downloadable!] (restricted)
    Other versions:
  4. Lucas Bretschger & Thomas M. Steger, 2004. "The dynamics of economic integration : theory and policy," CER-ETH Economics working paper series 04/32, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich. [Downloadable!]
    Other versions:
  5. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August. [Downloadable!] (restricted)
    Other versions:
  6. Raouf, BOUCEKKINE & David de la Croix, 2004. "Modelling vintage structures with DDEs : principles and applications," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2004004, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
    Other versions:
  7. Timo Trimborn & Karl-Josef Koch & Thomas M. Steger, 2004. "Multi-dimensional transitional dynamics : a simple numerical procedure," CER-ETH Economics working paper series 04/35, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich. [Downloadable!]
    Other versions:
  8. Moritz Schularick & Thomas Steger, 2006. "Does Financial Integration Spur Economic Growth? New Evidence from the First Era of Financial Globalization," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
    Other versions:
  9. El-Hodiri, Mohamed A & Loehman, Edna & Whinston, Andrew B, 1972. "An Optimal Growth Model with Time Lags," Econometrica, Econometric Society, vol. 40(6), pages 1137-46, November. [Downloadable!] (restricted)
  10. Corrado Di Maria & Simone Valente, 2006. "The Direction of Technical Change in Capital-Resource Economies," CER-ETH Economics working paper series 06/50, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich. [Downloadable!]
    Other versions:
  11. Sjak Smulders & Lucas Bretschger & Hannes Egli, 2005. "Economic growth and the diffusion of clean technologies : explaining environmental Kuznets," CER-ETH Economics working paper series 05/42, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich. [Downloadable!]
  12. Lucas Bretschger & Sjak Smulders, 2003. "Sustainability and Substitution of Exhaustible Natural Resources. How resource prices affect long-term R&D investments," Working Papers 2003.87, Fondazione Eni Enrico Mattei. [Downloadable!]
    Other versions:
  13. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November. [Downloadable!] (restricted)
    Other versions:
  14. Boucekkine, Raouf, et al, 1998. " Creative Destruction, Investment Volatility, and the Average Age of Capital," Journal of Economic Growth, Springer, vol. 3(4), pages 361-84, December. [Downloadable!] (restricted)
    Other versions:
  15. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2000. "Vintage Human Capital, Demographic Trends and Endogenous Growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000007, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES). [Downloadable!]
    Other versions:
  16. Boucekkine, Raouf & Germain, Marc & Licandro, Omar, 1997. "Replacement Echoes in the Vintage Capital Growth Model," Journal of Economic Theory, Elsevier, vol. 74(2), pages 333-348, June. [Downloadable!] (restricted)
    Other versions:
  17. Boucekkine, Raouf & Licandro, Omar & Paul, Christopher, 1997. "Differential-difference equations in economics: On the numerical solution of vintage capital growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 21(2-3), pages 347-362. [Downloadable!] (restricted)
    Other versions:
  18. Karen Pittel & Amigues Jean-Pierre & Thomas Kuhn, 2005. "Endogenous growth and recycling : a material balance approach," CER-ETH Economics working paper series 05/37, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich. [Downloadable!]
  19. Peeters, Marga, 1996. "Investment Gestation Lags: The Difference between Time-to-Build and Delivery Lags," Applied Economics, Taylor and Francis Journals, vol. 28(2), pages 203-08, February. [Downloadable!] (restricted)
  20. Thomas M. Steger, 2003. "Economic Growth and Sectoral Change under Resource Reallocation Costs," CER-ETH Economics working paper series 03/30, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich. [Downloadable!]
  21. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January. [Downloadable!] (restricted)
    Other versions:
  22. Thomas M. Steger, 2006. "On the Mechanics of Economic Convergence," German Economic Review, Blackwell Publishing, vol. 7, pages 317-337, 08. [Downloadable!] (restricted)
    Other versions:
  23. Boucekkine, Raouf & Germain, Marc & Licandro, Omar & Magnus, Alphonse, 2001. "Numerical solution by iterative methods of a class of vintage capital models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(5), pages 655-669, May. [Downloadable!] (restricted)
    Other versions:
  24. de la Croix, David & Licandro, Omar, 1999. "Life expectancy and endogenous growth," Economics Letters, Elsevier, vol. 65(2), pages 255-263, November. [Downloadable!] (restricted)
    Other versions:
  25. Clive Bell & Hans Gersbach, 2006. "Growth and Enduring Epidemic Diseases," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
    Other versions:
  26. Fabrice Collard & Omar Licandro & Luis A. Puch, . "The short-run dynamics of optimal growth models with delays," Working Papers 2004-05, FEDEA. [Downloadable!]
    Other versions:
  27. Christian Bjørnskov & Axel Dreher & Justina Fischer, 2007. "The bigger the better? Evidence of the effect of government size on life satisfaction around the world," Public Choice, Springer, vol. 130(3), pages 267-292, March. [Downloadable!] (restricted)
    Other versions:
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
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