Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
Abstract : Often considered in the numerical simulations related to quantum control, the so-called monotonic schemes have not been so far much studied from the functional analysis point of view. Yet, these procedures provide 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 model in quantum control. Those 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.
Constructive solution of a bilinear quantum control problem
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