Overview Of Optimal Control Problem On Linear Schrodinger Equation

After 20 years of development, the linear Schrodinger equation control systems optimal control problem has made great development. The purpose of this article is to introduce the results in this regard. This paper is divided into six sections: Section I describes the physical meaning of Schr?dinger equation; Section II with the Hilbert-Schmidt operator Schrodinger equation control systems optimal control problem, given the existence of optimal solution; section III, the use of difference approximation methods to discuss a class of Schr?dinger equation control systems optimal control problem, proved the difference schemes of the two estimates, as well as to the functional difference approximation of the convergence and convergence rate; Section IV describes the optimal control of a class of Schrodinger equation systems with singular potential, given the existence of solutions, and the first order optimal conditions; Section V presents a class of nonstationary systems of the Schrodinger equation optimal control problem and the corresponding existence and uniqueness of the necessary and sufficient condition; section VI wants to solve the maximum problem of the Schrodinger equation systems optimal control problem, (the previous sections have been discussing is the minimum problem), to prove the existence and under certain conditions the uniqueness of the solving.