使用约束 zonotope 的线性离散时间描述子系统的集合状态估计与故障诊断
Set-based state estimation and fault diagnosis of linear discrete-time descriptor systems using constrained zonotopes
AI总结：
本文提出基于约束 zonotope 的线性描述子系统集值状态估计与主动故障诊断新方法，直接纳入状态变量线性静态约束，无需秩假设，在准确性与效率间取得合理权衡。
摘要：
本文提出了线性描述子系统集值状态估计和主动故障诊断的新方法。该算法基于约束 zonotope，它是 zonotope 的推广，能够描述强非对称凸集，同时保留 zonotope 的计算优势。此外，与区间、zonotope、椭球、平行多面体等其他集合表示不同，状态变量上的线性静态约束（描述子系统的典型特征）可以直接纳入约束 zonotope 的数学描述中。因此，与基于上述集合的现有方法相比，所提方法在状态估计中产生更准确的结果，且无需对描述子系统结构做秩假设，并在准确性和效率之间取得了合理的权衡。这些优势在两个数值算例中得到了突出展示。
英文摘要：
This paper presents new methods for set-valued state estimation and active fault diagnosis of linear descriptor systems. The algorithms are based on constrained zonotopes, a generalization of zonotopes capable of describing strongly asymmetric convex sets, while retaining the computational advantages of zonotopes. Additionally, unlike other set representations like intervals, zonotopes, ellipsoids, paralletopes, among others, linear static constraints on the state variables, typical of descriptor systems, can be directly incorporated in the mathematical description of constrained zonotopes. Therefore, the proposed methods lead to more accurate results in state estimation in comparison to existing methods based on the previous sets without requiring rank assumptions on the structure of the descriptor system and with a fair trade-off between accuracy and efficiency. These advantages are highlighted in two numerical examples.
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