论文标题
连贯的量子LQG控制器与Luenberger动力学
Coherent quantum LQG controllers with Luenberger dynamics
论文作者
论文摘要
本文涉及一致的量子线性季度高斯控制问题，即最大程度地减少无限马均方根成本，用于无测量的量子介导的量子植物与稳定量子控制器的量子植物的互连。植物和控制器是多模量量子谐波振荡器，由线性量子随机微分方程控制，并彼此耦合以及真空状态下的外部多通道波索克场。我们讨论了量子物理可实现条件与与经典分离原理相关的Luenberger结构之间的相互作用。这导致对控制器增益矩阵的二次约束，该矩阵是在控制器变量的规范表示中的交换转换框架中提出的。对于使用Luenberger Dynamics的相干量子控制器类别，我们以代数方程式获得最佳的一阶必要条件，涉及矩阵值的Lagrange乘数。
This paper is concerned with the coherent quantum linear-quadratic-Gaussian control problem of minimising an infinite-horizon mean square cost for a measurement-free field-mediated interconnection of a quantum plant with a stabilising quantum controller. The plant and the controller are multimode open quantum harmonic oscillators, governed by linear quantum stochastic differential equations and coupled to each other and the external multichannel bosonic fields in the vacuum state. We discuss an interplay between the quantum physical realizability conditions and the Luenberger structure associated with the classical separation principle. This leads to a quadratic constraint on the controller gain matrices, which is formulated in the framework of a swapping transformation for the conjugate positions and momenta in the canonical representation of the controller variables. For the class of coherent quantum controllers with the Luenberger dynamics, we obtain first-order necessary conditions of optimality in the form of algebraic equations, involving a matrix-valued Lagrange multiplier.
