Аннотация:From the text: “We consider the optimal control problem of the system
x ˙=f(x,u),u∈V,dimu=m;x∈ℝ n ,x(t 0 )=x 0 ,x(t 1 )=x 1 ·(1)
The optimality of control is determined by the functional
J=∫ t 1 t 2 f 0 (x(t),u(t),t)dt·(2)
A control is optimal if it transfers the system from the point x 0 to a point x 1 and minimizes the functional J. This paper reduces the optimal control problem to a variational problem of finding a constrained extremum of the functional, which can be solved by the Lagrange multiplier method. The main difficulty connected with the fact that the controls u(t) are restricted to a domain is overcome by introducing new controls that are not constrained”.