Optimal control of a linear stochastic Schrödinger equation

Pages: 437 - 446, Issue special, November 2013

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Diana Keller - Martin Luther University Halle-Wittenberg, Faculty of Natural Sciences II, Institute of Mathematics, D - 06099 Halle (Saale), Germany (email)

Abstract: This paper concerns a linear controlled Schrödinger equation with additive noise and corresponding initial and Neumann boundary conditions. The existence and uniqueness of the variational solution of this Schrödinger problem and some of its properties will be discussed. Furthermore, a given objective functional shall be minimized by an optimal control. Though, instead of the control only the solution of the controlled Schrödinger problem appears explicitly in the objective functional. Based on the adjoint problem of the stochastic Schrödinger problem, a gradient formula is developed.

Keywords:  Linear stochastic Schrödinger equation, optimal control, adjoint problem, gradient method.
Mathematics Subject Classification:  Primary: 60H15, 93E20, 35Q55; Secondary: 35Q40.

Received: August 2012; Published: November 2013.