dorsal/arxiv
View SchemaHamilton-Jacobi-Bellman equations for Quantum Filtering and Control
| Authors | J. Gough, V. P. Belavkin, O. G. Smolyanov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502155 |
| URL | https://arxiv.org/abs/quant-ph/0502155 |
| DOI | 10.1088/1464-4266/7/10/006 |
| Journal | J. Opt. B: Quantum Semiclass. Opt. 7 S237-S244 (2005) |
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.
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"abstract": "We exploit the separation of the filtering and control aspects of quantum\nfeedback control to consider the optimal control as a classical stochastic\nproblem on the space of quantum states. We derive the corresponding\nHamilton-Jacobi-Bellman equations using the elementary arguments of classical\ncontrol theory and show that this is equivalent, in the Stratonovich calculus,\nto a stochastic Hamilton-Pontryagin setup. We show that, for cost functionals\nthat are linear in the state, the theory yields the traditional Bellman\nequations treated so far in quantum feedback.",
"arxiv_id": "quant-ph/0502155",
"authors": [
"J. Gough",
"V. P. Belavkin",
"O. G. Smolyanov"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"doi": "10.1088/1464-4266/7/10/006",
"journal_ref": "J. Opt. B: Quantum Semiclass. Opt. 7 S237-S244 (2005)",
"title": "Hamilton-Jacobi-Bellman equations for Quantum Filtering and Control",
"url": "https://arxiv.org/abs/quant-ph/0502155"
},
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