Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
752860 | Systems & Control Letters | 2008 | 12 Pages |
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 Łojasiewicz 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.