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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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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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