  The article is devoted to the problem of applying the maximum principle for
finding optimal control parameters in simulation tasks of interest for a
variety of engineering and industrial systems and processes. Especially
important is the problem for such systems where it is practically impossible to
organize a control system because of an unknown model or because it is
impossible to strictly follow the specified trajectories of control parameters
in each particular case. A so-called delta-procedure is constructed that
converges and allows one to obtain an approximation and optimal control of the
system in a finite number of steps with a given accuracy delta. The theorem on
the delta-procedure is proved and illustrative examples are given. Some
features of the application of the proposed algorithm to real problems of
simulation control are discussed, e.g. the optimal number of points dividing
the time interval under consideration, and tasks for further individual
research.
