Abstract
In this paper, an optimal control problem was taken up for a stationary equation of quasi optic. For the stationary equation of quasi optic, at first judgment relating to the existence and uniqueness of a boundary value problem was given. By using this judgment, the existence and uniqueness of the optimal control problem solutions were proved. Then we state a necessary condition to an optimal solution. We proved differentiability of a functional and obtained a formula for its gradient. By using this formula, the necessary condition for solvability of the problem is stated as the variational principle.
Highlights
1 Introduction Optimal control theory for the quantum mechanic systems described with the Schrödinger equation is one of the important areas of modern optimal control theory
A stationary quasi-optics equation is a form of the Schrödinger equation with complex potential
Optimal control problem for nonstationary Schrödinger equation of quasi optics was investigated for the first time in [ ]
Summary
Optimal control theory for the quantum mechanic systems described with the Schrödinger equation is one of the important areas of modern optimal control theory. √ where i = – , a > , l > , L > , α ≥ , b ≥ , b > , d > , d > are numbers, x ∈ [ , l], z ∈ [ , L], z = ( , l) × ( , z), = L, y(x), f (x, z) are complex valued measurable functions and satisfy the conditions f ∈ L ( ), ( ) Theorem Let us accept that the conditions of Theorem hold and y ∈ L ( , l) is a given function.
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