Existence results without convexity conditions for general problems of optimal control with singular components

Abstract

This note presents a new, quick approach to existence results without convexity conditions for optimal control problems with singular components in the sense of [11.], 438–485). Starting from the resolvent kernel representation of the solutions of a linear integral equation, a version of Fatou's lemma in several dimensions is shown to lead directly to a compactness result for the attainable set and an existence result for a Mayer problem. These results subsume those of [12.], 110–117), [13.], 74–101), [10.], [7.], 319–331) and [1.], 63–79).