Numerical solution of optimal control problems with constant control delays

Ulrich Brandt-Pollmann, Ralph Winkler, Sebastian Sager, Ulf Moslener and Johannes P. Schlöder
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Ulrich Brandt-Pollmann: Interdisciplinary Center for Scientific Computing, University of Heidelberg, Germany
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

No 06/59, CER-ETH Economics working paper series from CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich

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 (search for similar items in EconPapers)
JEL-codes: C61 C63 (search for similar items in EconPapers)
Pages: 26 pages
Date: 2006-10
New Economics Papers: this item is included in nep-cmp
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Related works:
Journal Article: Numerical Solution of Optimal Control Problems with Constant Control Delays (2008)
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