State Constraints in Convex Control Problems of Bolza

Abstract

Methods of convex analysis are applied to certain problems of Lagrange and Bolza in optimal control. Conditions characterizing optimal arcs are obtained without the usual differentiability assumptions on the data in the problem. Special existence theorems are proved. A dual control problem is formulated in terms of adjoint arcs which are not necessarily absolutely continuous, but of bounded variation, so as to allow for jumps caused by the presence of state contraints in the primal problem.