Concerning Synthesis of Controlled Systems and Alternativeness of Solutions for a Class of Degenerated Variational Problems. I

A variational problem of the synthesis of the closed controlled system with the known properties is formulated for the simpliest class of the controlled systems – determinated and completely supervised systems. The peculiarities of the studied class of variational problems in particular those concerning the degeneration are stressed. New approach to the problem of finding the degenerated variational problem solutions in non-parametric form is proposed. Jn the particular case the initial problem of the optimum control synthesis is reduced to the problem of finding numerical solutions of Bellman functional equation.