线区域多面体：用于无界和描述符系统状态估计与故障诊断的工具
Line zonotopes: A tool for state estimation and fault diagnosis of unbounded and descriptor systems
AI总结：
本文提出线区域多面体表示无界集合，扩展约束区域多面体至不稳定或不可观测的线性描述符系统，实现状态估计与主动故障诊断，并通过可达管扩展减少保守性。
摘要：
本文提出了针对线性描述符系统（LDS）的基于集合的状态估计和主动故障诊断（AFD）的新方法。与区间、椭球和区域多面体不同，约束区域多面体（CZs）可以将描述符系统典型的对状态变量的线性静态约束直接纳入其数学表示中，从而产生更不保守的包络。然而，对于不稳定或不完全可观测的LDS，有界表示无法确保状态随时间推移的有效包络。为解决这一局限性，我们引入了线区域多面体，这是一种用于无界集合的新表示，它保留了CZs的关键性质，包括多项式时间复杂度缩减方法，同时能够描述条带、超平面以及整个n维欧几里得空间。这一扩展不仅将CZs的使用推广到无界场景，还能在稳定和不稳定情形下增强基于集合的估计和AFD。此外，我们将Rego等人（2020）的LDS的AFD方法扩展为在可达管上运行，而非仅考虑所研究时间范围最终时刻的可达集。这减少了输入分离中的保守性，并能够基于整个输出序列进行更准确的故障诊断。通过数值示例证明了所提出方法相对于现有基于CZ方法的优势。
英文摘要：
This paper proposes new methods for set-based state estimation and active fault diagnosis (AFD) of linear descriptor systems (LDS). Unlike intervals, ellipsoids, and zonotopes, constrained zonotopes (CZs) can directly incorporate linear static constraints on state variables - typical of descriptor systems - into their mathematical representation, leading to less conservative enclosures. However, for LDS that are unstable or not fully observable, a bounded representation cannot ensure a valid enclosure of the states over time. To address this limitation, we introduce line zonotopes, a new representation for unbounded sets that retains key properties of CZs, including polynomial time complexity reduction methods, while enabling the description of strips, hyperplanes, and the entire n-dimensional Euclidean space. This extension not only generalizes the use of CZs to unbounded settings but can also enhance set-based estimation and AFD in both stable and unstable scenarios. Additionally, we extend the AFD method for LDS from Rego et al. (2020) to operate over reachable tubes rather than solely on the reachable set at the final time of the considered horizon. This reduces conservatism in input separation and enables more accurate fault diagnosis based on the entire output sequence. The advantages of the proposed methods over existing CZ-based approaches are demonstrated through numerical examples.
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