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 socalled 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
timediscretized 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. 





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