Computation of optimal singular controls

A class of singular control problems is made nonsingular by the addition of an integral quadratic functional of the control to the cost functional; a parameter
\epsilon > 0
multiplies this added functional. The resulting nonsingular problem is solved for a monotonically decreasing sequence
\{\epsilon; \epsilon_{1} > \epsilon_{2} > ... > \epsilon_{k} > 0\}
. As
k \rightarrow \infty
and
\epsilon_{k} \rightarrow 0
the solution of the modified problem tends to the solution of the original singular problem. A variant of the method which does not require that
\epsilon \rightarrow 0
is also presented. Four illustrative numerical examples are described.