Singular control

Summary

A singular control is an optimal control, or a candidate for one, on a time interval where the maximum principle gives no information. There the maximum condition of Pontryagin's maximum principle does not determine the control value. This happens when the Hamiltonian is affine in the control. The coefficient of the control, called the switching function, then vanishes on a whole interval. On such an interval the control usually takes interior values, unlike a bang–bang control. Singular arcs are found by differentiating the switching function in time until the control appears.