Optimal control for Schrodinger's equation with pure imaginary coefficient in the nonlinear part of the equation

摘要

Work is devoted study of a problem of optimal control for a Schrodinger equation with purely imaginary factor in a nonlinear part of this equation where control is quadratically the summable function, and the criterion of quality is a functional of Lions. With that end in view at first the correctness of statement of the reduced problem is investigated and the correctness of statement of a problem of optimum control is studied. Differentiability of a functional of Lions is investigated and the necessary condition of an optimality in the form of a variation inequality is established.