OPTIMAL BOUNDARY CONTROL FOR A SCHRODINGER EQUATION

In this paper we look for an answer to the question: To which extent can the solution of the Schrodinger equation be perturbed by the action of the Neumann boundary controls at a given final time in order to reach a given final target? Showing ill-posedness of the problem and after regularization, we get the Frechet differentiability and find the gradient of the new cost functional in terms of the solution of the adjoint problem. We constitute the minimizing sequence by the method of the projection of the gradient and prove its convergence to the optimal solution.