SIAM Journal on Control and Optimization, Volume 59, Issue 1, Page 669-692, January 2021.
In this paper, we consider $N$-level quantum angular momentum systems interacting with electromagnetic fields undergoing quantum nondemolition measurements in continuous-time. We suppose unawareness of the initial state and physical parameters, entailing the introduction of an additional state representing the estimated quantum state. The evolution of the quantum state and its estimation is described by a coupled stochastic master equation. Here, we study the asymptotic behavior of such a system in the presence of a feedback controller. We provide sufficient conditions on the feedback controller and on the estimated parameters that guarantee exponential stabilization of the coupled stochastic system toward an eigenstate of the measurement operator. Furthermore, we estimate the corresponding rate of convergence. We also provide parametrized feedback laws satisfying such conditions. Our results show the robustness of the feedback stabilization strategy considered in [W. Liang, N. H. Amini, and P. Mason, SIAM J. Control Optim., 57 (2019), pp. 3939--3960] in the case of imprecise initialization of the estimated state and with respect to the unknown physical parameters.

中文翻译：

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N级量子自旋系统的鲁棒反馈镇定

SIAM控制与优化杂志，第59卷，第1期，第669-692页，2021年1月。
在本文中，我们考虑$ N $级量子角动量系统与连续时间进行量子非爆破测量的电磁场相互作用。我们假设不了解初始状态和物理参数，因此需要引入表示估计量子状态的附加状态。量子态的演化及其估计由耦合的随机主方程描述。在这里，我们研究存在反馈控制器时这种系统的渐近行为。我们在反馈控制器和估计的参数上提供了足够的条件，以保证耦合的随机系统对测量操作员的本征态呈指数稳定。此外，我们估计相应的收敛速度。我们还提供满足此类条件的参数化反馈定律。我们的结果表明，在[W. Liang，NH Amini，和P.Mason，SIAM J.Control Optim。，57（2019），pp。3939--3960]。