Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control

@misc{citeulike:106608, abstract = {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.}, author = {Gough, J. and Belavkin, V. and Smolianov, O. }, citeulike-article-id = {106608}, eprint = {quant-ph/0502155}, keywords = {bellman, hamilton-jacobi, pontryagin, quantum-control, quantum-filtering, stratonovich}, month = {February}, posted-at = {2005-02-28 16:52:50}, priority = {2}, title = {Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control}, url = {http://arxiv.org/abs/quant-ph/0502155}, year = {2005} }

TY - ELEC ID - citeulike:106608 L3 - citeulike-article-id:106608 TI - Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control N2 - 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. KW - bellman KW - hamilton-jacobi KW - pontryagin KW - quantum-control KW - quantum-filtering KW - stratonovich AU - Gough, J AU - Belavkin, V AU - Smolianov, O PY - 2005/02/24/ UR - http://arxiv.org/abs/quant-ph/0502155 ER -