Performance-Robustness Tradeoffs in Adversarially Robust Linear-Quadratic Control
Performance-Robustness Tradeoffs in Adversarially Robust Linear-Quadratic Control
复制标题
DOI：
10.1109/cdc51059.2022.9992393
复制
发表时间：
2022-03
期刊：
影响因子：
--
通讯作者：
Bruce Lee;Thomas Zhang;Hamed Hassani;N. Matni
中科院分区：
文献类型：
--
作者：
Bruce Lee;Thomas Zhang;Hamed Hassani;N. Matni
虽然 ${\mathcal{H}_\infty }$ 方法可以引入针对最坏情况扰动的鲁棒性，但它们在传统随机扰动下的标称性能通常会急剧下降。尽管众所周知，标称性能和稳健性之间存在这种基本权衡，但尚未对其进行定量表征。为了解决这个问题，我们借鉴机器学习中日益普遍的对抗训练概念来构建一类控制器，这些控制器针对由混合随机和最坏情况分量组成的干扰进行了优化。我们发现这个问题承认一个固定最优控制器，它具有与次优 ${\mathcal{H}_\infty }$ 解决方案密切相关的简单分析形式。然后，我们提供定量的性能-鲁棒性权衡分析，其中系统理论特性（例如可控性和稳定性）以可解释的方式明确体现。这为从业者提供了一般指导，用于根据先验系统知识确定要合并的鲁棒性程度。我们通过将控制器的性能与标准基线进行比较并绘制权衡曲线来实证验证我们的结果。
While ${\mathcal{H}_\infty }$ methods can introduce robustness against worst-case perturbations, their nominal performance under conventional stochastic disturbances is often drastically reduced. Though this fundamental tradeoff between nominal performance and robustness is known to exist, it has not been quantitatively characterized. Toward addressing this issue, we borrow from the increasingly ubiquitous notion of adversarial training from machine learning to construct a class of controllers which are optimized for disturbances consisting of mixed stochastic and worst-case components. We find that this problem admits a stationary optimal controller that has a simple analytic form closely related to suboptimal ${\mathcal{H}_\infty }$ solutions. We then provide a quantitative performance-robustness tradeoff analysis, in which system-theoretic properties such as controllability and stability explicitly manifest in an interpretable manner. This provides practitioners with general guidance for determining how much robustness to incorporate based on a priori system knowledge. We empirically validate our results by comparing the performance of our controller against standard baselines, and plotting tradeoff curves.