论文标题
遗憾
On the Regret of $\mathcal{H}_{\infty}$ Control
论文作者
论文摘要
$ \ MATHCAL {H} _ {\ infty} $合成方法是一种基石强大的控制设计技术，但在某些情况下是保守的。本文的目的是通过采用受到在线学习后悔启发的方法来量化控制器对最坏情况的额外成本。我们将\ textit {disction-真实差距}定义为预测的最坏情况干扰信号与实际实现之间的差异。遗憾的表现为以此\ textit {gap}的规范的规模扩展，事实证明，该结构与确定性等效控制器具有不准确的预测，以\ textit {预测错误} norm n narm在此处获得。
The $\mathcal{H}_{\infty}$ synthesis approach is a cornerstone robust control design technique, but is known to be conservative in some cases. The objective of this paper is to quantify the additional cost the controller incurs planning for the worst-case scenario, by adopting an approach inspired by regret from online learning. We define the \textit{disturbance-reality gap} as the difference between the predicted worst-case disturbance signal and the actual realization. The regret is shown to scale with the norm of this \textit{gap}, which turns out to have a similar structure to that of the certainty equivalent controller with inaccurate predictions, obtained here in terms of the \textit{prediction error} norm.
