On the necessary conditions for optimal control of retarded systems

In this paper we derive necessary conditions, in the form of a maximum principle, for the optimal control of nonlinear, finitely retarded functional differential equations with function-space boundary conditions. We establish these conditions in a setting which guarantees the existence of regular multipliers, admits pointwise control constraints, and, with added restrictions, ensures nontriviality of the multipliers.The majority of this work was done while the first author was guest at the Institute für Numerische und Angewandte Mathematik der Universität Göttingen, Göttingen, BRD.