Global search in the optimal control problem with a terminal objective functional represented as the difference of two convex functions

A nonconvex optimal control problem is examined for a system that is linear with respect to state and has a terminal objective functional representable as the difference of two convex functions. A new local search method is proposed, and its convergence is proved. A strategy is also developed for the search of a globally optimal control process, because the Pontryagin and Bellman principles as applied to the above problem do not distinguish between the locally and globally optimal processes. The convergence of this strategy under appropriate conditions is proved.