We study here the delay problem studied in  and , originating from . The aim is to find the optimal harvesting of a renewable ressource whose growth follows a logistic function. Denoting the biomass of population and the harvesting effort, the optimal control problem is stated as
with the harvesting cost , the growth rates , the discount rate and market price , and the growth delay . Bocop can handle the delayed term without having to perform the classical Guinn transformation (), but for a fixed final time only. Therefore we perform a batch of optimizations for , and iterate the process for to find a better estimate of the optimal time. Batch optimizations indicate an optimal final time with an objective .
Fig1: Delay problem. Cost function with respect to final time T.
Fig2: Delay problem. Optimal state and control for T = 12.24.
 A. Boccia, P. Falugi, H. Maurer, and R. Vinter. Free time optimal control problems with time delays. pages 520–525. IEEE, 2013.
 L. Goellmann, D. Kern, and H. Maurer. Optimal control problems with delays in state and control variables subject to mixed control-state constraints. Optimal Control Applications and Methods, 30(4):341–365, 2009.
 T. Guinn. Reduction of delayed optimal control problems to non-delayed problems. Journal of Optimization Theory and Applications, 18(3):371–377, 1976.
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