We investigate the laser induced population transfer between electronic states of Na-2 molecules which are subject to additional perturbations by an environment. In a former paper [S. Grafe, M. Erdmann, V. Engel, Phys. Rev. A 72 ( 2005) 013404] it was shown that within the formalism of Local Control Theory, laser fields can be constructed which are able to selectively transfer population from the electronic ground to a target excited electronic state. Here, we address the question in how far the efficiency of the control process is influenced by additional perturbations. Therefore, we employ a stochastic Schrodinger equation including a fluctuation-term in the Hamiltonian. (c) 2009 Elsevier B.V. All rights reserved.