Nonlocal improving controls of nonlinear discrete systems

The article is devoted to an approach for nonlocal improvement in general nonlinear optimal control problems with discrete systems on basis of the fundamental theory by V.F.Krotov and the state regularization (this term is by V.A.Srochko). The sufficient conditions of nonlocal improvement are formulated, including the regularized form. There are some improvement algorithms, which use special discrete algebraic boundary value problems with maximizing and projecting mappings for Hamilton's function, and also an algorithm for construction the sequence of approximations in the space of controls. There are examples of improving "ordinary" processes and process, which satisfies the discrete maximum principle.