ABSTRACT
The determination of mathematical models is connected to the passage to the limit. The Cauchy principle is the practical method of proving of the convergence for the real numbers sequence. The completion procedure, which is the basis of the sequential method, was tested on an incomplete space of rational numbers. The chapter considers the non-uniqueness of the optimal control and the well-posedness of optimization problems in the sense of Tikhonov, which clarifies the structure of sequentially optimal controls. The sequential controls are the equivalence classes of the fundamental sequences of usual controls. Each regular sequential control contains a stationary sequence of usual controls. The sequential controls are usually singular as the typical real numbers are irrational. The optimal control problem is insolvable if the sequentially optimal control is singular. The transition from finding the nonexistent optimal control to finding the existing sequentially optimal control can give a basis for determining the minimizing sequences that generate it.
