Constructive solution of a bilinear optimal control problem for a Schrodinger equation

摘要

Often considered in numerical simulations related to the control of quantum systems, the so-called monotonic schemes have not been so far much studied from the functional analysis point of view. Yet, these procedures provide an efficient constructive method for solving a certain class of optimal control problems. This paper aims both at extending the results already available about these algorithms in the finite-dimensional case (i.e., the time-discretized case) and at completing those of the continuous case. This paper starts with some results about the regularity of a functional related to a wide class of models in quantum chemistry. These enable us to extend an inequality due to Lojasiewicz to the infinite-dimensional case. Finally, some inequalities proving the Cauchy character of the monotonic sequence are obtained, followed by an estimation of the rate of convergence. (C) 2007 Elsevier B.V. All rights reserved.