Numerical Solution of Optimal Control Problems With Constant Control Delays

CER-ETH - Center of Economic Research at ETH Zurich, Working Paper No. 06/59

26 Pages Posted: 30 Nov 2006

See all articles by Ullrich Brandt-Pollmann

Ullrich Brandt-Pollmann

University of Heidelberg - Interdisciplinary Institute for Environmental Economics

Ralph Winkler

University of Bern - Department of Economics; University of Bern - Oeschger Centre for Climate Change Research

Sebastian Sager

Heidelberg University - Interdisciplinary Center for Scientific Computing

Ulf Moslener

Frankfurt School of Finance & Management gemeinnützige GmbH

Johannes Schloeder

Interdisciplinary Center for Scientific Computing

Multiple version iconThere are 2 versions of this paper

Date Written: October 2006

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.

Keywords: delayed differential equations, delayed optimal control, numerical optimization, time-to-build

JEL Classification: C63, C61

Suggested Citation

Brandt-Pollmann, Ullrich and Winkler, Ralph and Sager, Sebastian and Moslener, Ulf and Schloeder, Johannes, Numerical Solution of Optimal Control Problems With Constant Control Delays (October 2006). CER-ETH - Center of Economic Research at ETH Zurich, Working Paper No. 06/59. Available at SSRN: https://ssrn.com/abstract=948137 or http://dx.doi.org/10.2139/ssrn.948137

Ullrich Brandt-Pollmann (Contact Author)

University of Heidelberg - Interdisciplinary Institute for Environmental Economics ( email )

Grabengasse 1
Heidelberg
Germany

Ralph Winkler

University of Bern - Department of Economics ( email )

Schanzeneckstrasse 1
Bern, 3001
Switzerland
+41 31 631 4508 (Phone)

HOME PAGE: http://www.ralph-winkler.de

University of Bern - Oeschger Centre for Climate Change Research ( email )

Zähringerstrasse 25
Bern, 3012
Switzerland

Sebastian Sager

Heidelberg University - Interdisciplinary Center for Scientific Computing ( email )

Im Neuenheimer Feld 368
Heidelberg, D-69120
Germany

Ulf Moslener

Frankfurt School of Finance & Management gemeinnützige GmbH ( email )

Adickesallee 32-34
Frankfurt am Main, 60322
Germany

Johannes Schloeder

Interdisciplinary Center for Scientific Computing ( email )

Im Neuenheimer Feld 368
Heidelberg, D-69120
Germany

HOME PAGE: http://www.iwr.uni-heidelberg.de/

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