Optimal control of quantum stochastic systems in fermion fields: The Pontryagin-type maximum principle (II)
Optimization and Control
2024-09-04 v1 Functional Analysis
Abstract
In the present paper, by using the relaxed transposition method[29], we solve the second-order adjoint equations, corresponding to the optimal control of quantum stochastic systems in fermion fields, which plays the fundamental roles in the study of the Pointryagin-type maximum principle in quantum stochastic optimal control. The second-order adjoint equation is a backard operator valued quantum stochastic differential equation, which has no definition in the algebra of bounded operators, and the solution derived from the relaxed transposition method makes sense in W*-topology.
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Cite
@article{arxiv.2409.01684,
title = {Optimal control of quantum stochastic systems in fermion fields: The Pontryagin-type maximum principle (II)},
author = {Penghui Wang and Shan Wang},
journal= {arXiv preprint arXiv:2409.01684},
year = {2024}
}
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29 pages