不确定线性量子系统的鲁棒观测器
Robust observer for uncertain linear quantum systems
摘要：
在量子动力学滤波理论中，最大的问题之一是由量子随机微分方程表示的底层系统动力学必须精确地知道，以便相应的滤波器提供最佳性能;然而，这种假设通常是不现实的。因此，在本文中，我们考虑了一类线性量子系统的时变范数有界参数不确定性，然后提出了一个鲁棒观测器，使得估计误差的方差是保证在一定的范围内。虽然在线性情况下，许多经典的控制理论可以应用到量子系统，量子鲁棒观测器在本文中得到的没有一个经典的模拟，由于系统的特定结构的不确定性。此外，通过考虑一个典型的量子控制问题，我们表明，所提出的鲁棒观测器是相当强大的对系统的参数不确定性，即使当其他估计-最优卡尔曼滤波器和风险敏感的观测器-在估计失败。
英文摘要：
In the theory of quantum dynamical filtering, one of the biggest issues is that the underlying system dynamics represented by a quantum stochastic differential equation must be known exactly in order that the corresponding filter provides an optimal performance; however, this assumption is generally unrealistic. Therefore, in this paper, we consider a class of linear quantum systems subjected to time-varying norm-bounded parametric uncertainties and then propose a robust observer such that the variance of the estimation error is guaranteed to be within a certain bound. Although in the linear case much of classical control theory can be applied to quantum systems, the quantum robust observer obtained in this paper does not have a classical analogue due to the system's specific structure with respect to the uncertainties. Moreover, by considering a typical quantum control problem, we show that the proposed robust observer is fairly robust against a parametric uncertainty of the system even when the other estimators--the optimal Kalman filter and risk-sensitive observer--fail in the estimation.
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