On the existence of a generalized optimal synthesis for linear quadratic singular optimal control problems with a fixed terminal point

Abstract

Uses the techniques of jump vectors, distributional inputs, decompositions of the state, control, and output spaces as direct sums of proper subspaces as well as the existence of an optimal synthesis for linear quadratic regular optimal control problems with a fixed terminal point to give a simple and constructive proof of the existence of a generalized optimal synthesis for linear quadratic singular optimal control problems with a fixed terminal point.