Numerical procedure for solving a class of singular optimal control problems

We consider the numerical solution of a class of optimal control problems where the optimal control policy involves singular arcs. An algorithm for determining a sub-optimal sequence of bang–bang and singular arcs and the exact switching times for the control is developed. We assume that the singular control depends on both the state and the costate of the problem. The algorithm is based on the solution of a two point boundary value problem arising from application of the minimum principle. A recently developed transformation technique is also employed to allow calculation of the corresponding switching times. Numerical examples are solved to illustrate the proposed algorithm.