标题： 概率鲁棒性在间隙度量中 显示英文标题

标题： Probabilistic Robustness in the Gap Metric

摘要： 影响动态系统的不确定性给估计旨在控制此类不确定系统的控制器的可实现性能带来了重大挑战。 当不确定性具有随机性质时，无法获得针对不确定性的控制器鲁棒性的硬性保证。 这一问题为概率鲁棒控制方法的发展奠定了基础。 在本文中，我们利用已知的名义模型与不确定系统未知扰动模型之间的差距度量作为衡量控制器鲁棒性的工具，并在存在随机不确定性的情况下将差距表述为一个随机变量。 本文的主要结果包括给出差距超过已知阈值的概率界，随后是期望差距值的界以及基于差距度量的概率鲁棒稳定性。 此外，我们还提供了在差距不确定性下的概率控制器性能认证以及对可实现$\mathcal{H}_{\infty}$鲁棒性的概率保证。 在许多地方提供了数值仿真以展示所提出的方法。 显示英文摘要

摘要： Uncertainties influencing the dynamical systems pose a significant challenge in estimating the achievable performance of a controller aiming to control such uncertain systems. When the uncertainties are of stochastic nature, obtaining hard guarantees for the robustness of a controller aiming to hedge against the uncertainty is not possible. This issue set the platform for the development of probabilistic robust control approaches. In this work, we utilise the gap metric between the known nominal model and the unknown perturbed model of the uncertain system as a tool to gauge the robustness of a controller and formulate the gap as a random variable in the setting with stochastic uncertainties. Main results of this paper includes giving probabilistic bound on the gap exceeding a known threshold followed by bounds on the expected gap value and probabilistic robust stability in terms of the gap metric. Further, we also provide a probabilistic controller performance certification under gap uncertainty and probabilistic guarantee on the achievable $\mathcal{H}_{\infty}$ robustness. Numerical simulations are provided at many places to demonstrate the proposed approach.