Quantum stochastic linear quadratic control theory: Closed-loop solvability
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909514326867968 |
|---|---|
| author | Penghui, Wang Shan, Wang Shengkai, Zhao |
| author_facet | Penghui, Wang Shan, Wang Shengkai, Zhao |
| contents | In this paper, we investigate the closed-loop solvability of the quantum stochastic linear quadratic optimal control problem. We derive the Pontryagin maximum principle for the linear quadratic control problem of infinite-dimensional quantum stochastic systems. The equivalence between unique closed-loop solvability for quantum stochastic linear quadratic optimal control problems and the well-posedness of the corresponding quantum Riccati equations is established. Notably, although the quantum Riccati equation is an infinite-dimensional deterministic operator-valued ordinary differential equation, classical methods are not applicable. Inspired by Lü and Zhang's approach [Q. Lü and X. Zhang, Probability Theory and Stochastic Modelling, 101. Springer, Cham, (2021) \& Mem. Amer. Math. Soc. 294 (2024)] to stochastic Riccati equations, we prove the existence and uniqueness of its solutions. The results provide a theoretical foundation for the optimal design of quantum control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19666 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum stochastic linear quadratic control theory: Closed-loop solvability Penghui, Wang Shan, Wang Shengkai, Zhao Optimization and Control Functional Analysis 46L53, 49N10, 81S25, 93E20 In this paper, we investigate the closed-loop solvability of the quantum stochastic linear quadratic optimal control problem. We derive the Pontryagin maximum principle for the linear quadratic control problem of infinite-dimensional quantum stochastic systems. The equivalence between unique closed-loop solvability for quantum stochastic linear quadratic optimal control problems and the well-posedness of the corresponding quantum Riccati equations is established. Notably, although the quantum Riccati equation is an infinite-dimensional deterministic operator-valued ordinary differential equation, classical methods are not applicable. Inspired by Lü and Zhang's approach [Q. Lü and X. Zhang, Probability Theory and Stochastic Modelling, 101. Springer, Cham, (2021) \& Mem. Amer. Math. Soc. 294 (2024)] to stochastic Riccati equations, we prove the existence and uniqueness of its solutions. The results provide a theoretical foundation for the optimal design of quantum control. |
| title | Quantum stochastic linear quadratic control theory: Closed-loop solvability |
| topic | Optimization and Control Functional Analysis 46L53, 49N10, 81S25, 93E20 |
| url | https://arxiv.org/abs/2502.19666 |