Singular arcs occurring in optimal electric steel refining

A second-order nonlinear model of steel refining in an electric are furnace is formulated and optimized. Iterative computation using steepest descent shows the existence of an optimal singular arc, which is then found more precisely by directly applying necessary conditions for such an arc. When a soft (penalty-function) constraint on state is replaced by a hard constraint, a state-constrained arc is found which corresponds directly to the singular arc. The dependence of the singular arc on problem parameters is explored.