线性量子随机系统二次指数函数速率的状态空间计算
State-space computation of quadratic-exponential functional rates for linear quantum stochastic systems
摘要：
研究了多通道玻色子场驱动下线性量子随机系统中二次指数泛函的无限时域增长率。这种风险敏感的性能标准对系统变量的二次函数的积分施加指数惩罚，并且它们的最小化改善了系统相对于量子统计不确定性的鲁棒性，并且使其行为在尾部分布方面更加保守。为了在状态空间中计算量子电场的增长率，我们采用了真空输入场系统的不变高斯量子态的量子电场增长率的频域表示。QEF率与线性系统的无限级联产生的经典平稳高斯随机过程的类似泛函有关。该成形滤波器的截断允许通过求解代数李雅普诺夫方程的递归序列以及代数Riccati方程来以任何精度计算QEF速率。通过一个开放的量子谐振子的数值例子，说明了QEF率的状态空间计算及其与频域结果的比较。
英文摘要：
This paper is concerned with infinite-horizon growth rates of quadratic-exponential functionals (QEFs) for linear quantum stochastic systems driven by multichannel bosonic fields. Such risk-sensitive performance criteria impose an exponential penalty on the integral of a quadratic function of the system variables, and their minimization improves robustness properties of the system with respect to quantum statistical uncertainties and makes its behaviour more conservative in terms of tail distributions. We use a frequency-domain representation of the QEF growth rate for the invariant Gaussian quantum state of the system with vacuum input fields in order to compute it in state space. The QEF rate is related to a similar functional for a classical stationary Gaussian random process generated by an infinite cascade of linear systems. A truncation of this shaping filter allows the QEF rate to be computed with any accuracy by solving a recurrent sequence of algebraic Lyapunov equations together with an algebraic Riccati equation. The state-space computation of the QEF rate and its comparison with the frequency-domain results are demonstrated by a numerical example for an open quantum harmonic oscillator.
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