In optimal control, problems of singular control are problems that are difficult to solve because a straightforward application of Pontryagin's minimum principle fails to yield a complete solution. Only a few such problems have been solved, such as Merton's portfolio problem in financial economics or trajectory optimization in aeronautics. A more technical explanation follows.

The most common difficulty in applying Pontryagin's principle arises when the Hamiltonian, specifically:

is positive at some times, negative at others and is only zero instantaneously, then the solution is straightforward and is a bang-bang control switches from negative to positive.

is called the singular control is determined by the requirement that the singularity condition continues to hold. The resulting so-called singular arc, if it is optimal, will satisfy the Kelley condition:

Others refer to this condition as the generalized Legendre–Clebsch condition.

The term bang-singular control refers to a control that has a bang-bang portion as well as a singular portion.

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