On the computation of optimal singular controls

The addition of a perturbed-energy term to the original cost functional of optimal singular control problems in order to avoid difficulties associated with computing singular controls is assessed via a direct search iterative dynamic programming procedure. The limitation of the strategy is shown from a computational point of view and some guidelines in the selection of the perturbation parameter is given using three examples. It is demonstrated that many gradient-based methods may not be particularly suited for computing singular sub-arcs when perturbation methods are used.