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 parameterε > 0multiplies this added functional. The resulting nonsingular problem is solved for a monotonically decreasing sequence\{ε; ε₁ > ε₂ > ... > εₖ > 0\}. Ask → εₖ → 0the solution of the modified problem tends to the solution of the original singular problem. A variant of the method which does not require thatε → 0is also presented. Four illustrative numerical examples are described.