Numerical Solution of Optimal Control Problems with Constant Control Delays
Computational Economics, Vol. 31, pp. 181-206, 2008
27 Pages Posted: 14 Jan 2008 Last revised: 23 Aug 2008
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: Suggested Citation