频域方法界定Riccati方程扰动的界限
A Frequency Domain Approach to Bounding Riccati Equation Perturbations
- University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出频域方法，为离散代数Riccati方程在LQR数据扰动下的解差异提供显式界限，采用频域稳定性常数并放宽可检测性假设。
AI中文摘要：
离散代数Riccati方程（DARE）用于求解离散时间系统线性二次调节器（LQR）控制中的最优反馈增益。本文考虑LQR数据扰动对DARE解的影响。我们提出一种新的频域方法，以推导此类扰动下DARE解差异的显式界限。我们的界限与文献中近期出现的其他结果相似，但有两个区别。首先，我们使用一个频域常数来衡量闭环稳定程度，而其他结果则使用时域度量。其次，我们从对LQR状态代价矩阵的可检测性假设较弱出发。
英文摘要：
The discrete algebraic Riccati equation (DARE) is used to solve for the optimal feedback gain in linear-quadratic regulator (LQR) control of discrete-time systems. In this letter, we consider the effect of perturbations to the LQR data on the DARE solutions. We present a new frequency domain approach to derive an explicit bound on the difference in DARE solutions under such perturbations. Our bounds are similar to other results that have recently appeared in the literature with two distinctions. First, we use a frequency domain constant that measures the degree of closed-loop stability, in contrast to other results that use a time domain measure. Second, we start from weaker detectability assumptions on the LQR state cost matrix.
