Variational problem with complex coefficient of a nonlinear Schrödinger equation

An optimal control problem with final observation for systems governed by nonlinear Schrödinger equation

“…Similarly, in the case of r 2 (x, t, ψ) = r 2 (x, t), r 1 (x, t, ψ) = 0, r 0 (x, t, ψ) = r 0 (x, t, ψ) in the equation (1), a nonlinear Schrödinger equation is obtained from equation (1). The optimal control problems for the different variants of systems described by nonlinear Schrödinger equations were studied in the papers [8], [10][11][12], [16][17], [23,26]. Also, in the case of r 2 (x, t, ψ) = r 2 (x, t), r 1 (x, t, ψ) = r 1 (x, t), r 0 (x, t, ψ) = r 0 (x, t) in the equation (1), the optimal control problems for the different variants of systems described by linear Schrödinger equations obtained from equation (1) were examined in the papers [24][25].…”

A Note on Optimal Control Problem Governed by Schrödinger Equation

“…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.…”

“…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].…”