Optimal control of quantum stochastic systems in fermion fields: The Pontryagin-type maximum principle (II)
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910588398993408 |
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| author | Wang, Penghui Wang, Shan |
| author_facet | Wang, Penghui Wang, Shan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01684 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal control of quantum stochastic systems in fermion fields: The Pontryagin-type maximum principle (II) Wang, Penghui Wang, Shan Optimization and Control Functional Analysis 47C15, 81S25, 81Q93, 81V74 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. |
| title | Optimal control of quantum stochastic systems in fermion fields: The Pontryagin-type maximum principle (II) |
| topic | Optimization and Control Functional Analysis 47C15, 81S25, 81Q93, 81V74 |
| url | https://arxiv.org/abs/2409.01684 |