The singular control problem and approximate solutions

A method is presented which permits the solution of singular control problems by approximating the nonnormal system with a normal system. It is shown that the approximation can be made arbitrarily accurate. The optimal control of the approximate system is then determined and applied to the actual system. Bounds are obtained on the errors in boundary conditions and the degree of suboptimality brought about by the technique. The method is valid for minimum time and minimum fuel problems with linear constant plants. Examples are presented.