Optimal control problem for stationary quasi-optic equations

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.

A Note on Optimal Control Problem Governed by Schrödinger Equation

“…They analyzed existence and uniqueness theorems and optimality conditions for solution. These problems have since been widely studied by many researchers in [9][10][11][12][13][14].…”

“…Control theory is a very important interdisciplinary branch of electric-electronics engineering and applied mathematics that deals with the behavior of dynamical systems with inputs, outputs and feedback [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. From this point of view, optimal control theory, is an outstanding mathematical optimization method for deriving control policies.…”