Optimal control of a linear system whose quadratic performance criterion is singular

Two approaches to solution of the problem are discussed, the method of functional regularization and the method of extending the initial variational problem. For the former case a sequence of suboptimal controls is developed and a necessary and sufficient condition is obtained for the existence of optimal control in the class of measurable controls. For the latter case the optimal path is determined which satisfies a differential equation with a measure and proves to be a discontinuous function.