A Remark on the Continuity of the Measure Lagrange Multiplier in State Constrained Optimal Control Problems

Abstract

The article is focused on the necessary optimality condition in the form of Pontryagin's maximum principle for state constrained problems. A certain refinement to these conditions is made. More specifically, it has been noted that the measure-multiplier from the maximum principle is continuous under the regularity conditions imposed in cite{Pontryagin_1962}. The continuity of the measure-multiplier appears to be highly relevant for numerical implementations in the framework of indirect computational approach.