Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control
Gough, J. ; Belavkin, V. P. ; Smolyanov, O. G.
arXiv, 0502155 / Harvested from arXiv
Text on arXiv
We exploit the separation of the filtering and control aspects of quantum feedback control to consider the optimal control as a classical stochastic problem on the space of quantum states. We derive the corresponding Hamilton-Jacobi-Bellman equations using the elementary arguments of classical control theory and show that this is equivalent, in the Stratonovich calculus, to a stochastic Hamilton-Pontryagin setup. We show that, for cost functionals that are linear in the state, the theory yields the traditional Bellman equations treated so far in quantum feedback.
Publié le : 2005-02-24
Classification:  Quantum Physics,  Mathematical Physics 
@article{0502155,
     author = {Gough, J. and Belavkin, V. P. and Smolyanov, O. G.},
     title = {Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0502155}
}

Gough, J.; Belavkin, V. P.; Smolyanov, O. G. Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0502155/