Numerical solution methods for singular control with multiple state dependent forms

Abstract

We use several recently developed techniques along with two established optimal control softwares to solve a variation of a widely studied singular optimal control problem. The problem displays some interesting features from both the analytical and numerical point of view. In particular, we show that, during singular arcs, the optimal control takes on one of two distinct state dependent forms. We also demonstrate how the numerical solution methods can easily get trapped in what may appear to be local optima when applied to this problem.