On the computation of optimal singular and bang–bang controls

To avoid difficulties associated with the computation of optimal singular/bang–bang controls, a common approach is to add a perturbed energy term. The efficacy of this perturbation method is assessed here via a direct search iterative dynamic programming procedure. A potential limitation of the strategy is shown from a computational point of view, and some guidelines for selecting the perturbation parameter are provided using numerical examples. It is demonstrated that many gradient-based methods may not be well suited for computing singular/bang–bang controls when perturbation methods are used to solve optimal control problems in chemical process control.