Choosing Grid Points in Solving Singular Optimal Control Problems by Iterative Dynamic Programming

R. Luus (Canada)

Keywords

Optimal control; Fedbatch reactor; Iterative dynamic programming; Grid points; Singular control

Abstract

In using iterative dynamic programming to deter mine the optimal control policy of complex systems, the time interval is divided into P time intervals to convert the optimal control problem into an optimization problem involving P stages. We consider the parametrization, where in each time interval the control is kept constant, but the length of the time stage is allowed to vary, so that the length of each time stage is determined during the course of optimization. To determine the optimal feed rate for two fed-batch reactor models involving ethanol fermentation, it is found that more than one grid point is required at each time interval to get convergence to the vicinity of the global optimum. For these optimal control problems, it is considerably better to use random pertur bations in the control policy than uniform perturbations in order to generate the grid points.

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