标题： 鲁棒控制中的风险分析 -- 为概率鲁棒控制辩护 显示英文标题

标题： Risk Analysis in Robust Control -- Making the Case for Probabilistic Robust Control

摘要： 本文对鲁棒控制设计的核心“最坏情况”方法提出了批判性观点。我们认为，盲目接受最坏情况可能会导致比基于概率技术并包含内置风险因素的设计更加危险的设计。真正的问题在于建模。如果接受不确定性没有完美的数学模型，那么即使不能保证所有可能情况下的稳定性，概率方法也能带来更可靠的控制。我们的论述基于案例分析。我们首先证明最坏情况并不一定是“全面的”。事实上，我们表明，对于一些不确定的控制问题，要获得传统的鲁棒控制解，必须做出排除某些可行情况的假设。一旦确立了这一点，我们就认为在最坏情况设计中未考虑情况的风险大于概率方法中接受的风险是不常见的。通过一个例子，我们量化了风险，并表明最坏情况可能要危险得多。最后，我们将分析与现有的计算复杂性和概率鲁棒性结果相结合，论证确定性的最坏情况分析不一定是最优工具。 显示英文摘要

摘要： This paper offers a critical view of the "worst-case" approach that is the cornerstone of robust control design. It is our contention that a blind acceptance of worst-case scenarios may lead to designs that are actually more dangerous than designs based on probabilistic techniques with a built-in risk factor. The real issue is one of modeling. If one accepts that no mathematical model of uncertainties is perfect then a probabilistic approach can lead to more reliable control even if it cannot guarantee stability for all possible cases. Our presentation is based on case analysis. We first establish that worst-case is not necessarily "all-encompassing." In fact, we show that for some uncertain control problems to have a conventional robust control solution it is necessary to make assumptions that leave out some feasible cases. Once we establish that point, we argue that it is not uncommon for the risk of unaccounted cases in worst-case design to be greater than that of the accepted risk in a probabilistic approach. With an example, we quantify the risks and show that worst-case can be significantly more risky. Finally, we join our analysis with existing results on computational complexity and probabilistic robustness to argue that the deterministic worst-case analysis is not necessarily the better tool.