Optimal control problems with terminal functionals represented as the difference of two convex functions

Two control problems for a state-linear control system are considered: the minimization of a terminal functional representable as the difference of two convex functions (d.c. functions) and the minimization of a convex terminal functional with a d.c. terminal inequality contraint. Necessary and sufficient global optimality conditions are proved for problems in which the Pontryagin and Bellman maximum principles do not distinguish between locally and globally optimal processes. The efficiency of the approach is illustrated by examples.