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arXiv · 2409.01684

Optimal control of quantum stochastic systems in fermion fields: The Pontryagin-type maximum principle (II)

Penghui Wang·Shan Wang
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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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Penghui Wang, Shan Wang. 2024-09-03. Optimal control of quantum stochastic systems in fermion fields: The Pontryagin-type maximum principle (II). https://arxiv.org/abs/2409.01684

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