The study on the calculus of variations.

Abstract

A method of solving Lagrange problem with phase constraints for t he processes described by ordinary differential equations without the involvement of the Lagrange principle is supposed. Necessary and sufficient conditions for existence of solution of the variation problem are obtained, feasible control is found and optimal solu tion is constructed by narrowing the field of feasible controls. The basis of the proposed method for solving the variation probl em is the immersion principle. The essence of the immersion principle is that the origina l variation problem with the boundary conditions with phase and integral constraints is replaced by equivalent optimal control problem with a free right end of the trajectory. This approach is made possible by finding the general solution of a class of Fredholm int egral equations of the first order.