迈向物理混合系统
Towards Physical Hybrid Systems
AI总结：
本文提出物理混合系统概念，通过修改混合系统逻辑以消除时间测度零集的区分，从而将数学模型与物理现实重新统一，并开发证明演算以验证此类系统。
摘要：
一些混合系统模型由于数学上正确但物理上不合理的理由而不安全。例如，数学模型可能将系统标记为不安全，仅在太小的集合上，这些集合在物理上不重要。特别是，在物理系统（CPS）模型中，测度零集的差异对这些模型的数学安全性有重大影响，尽管这些差异在实际系统中没有实际影响。我们开发了“物理混合系统”（PHS）的概念，以帮助重新统一数学模型与物理现实。我们通过在混合系统逻辑（微分时间动态逻辑）中添加一个一等运算符来消除CPS模型中时间测度零集的区分。这种方法促进了建模，因为它允许验证更广泛的模型类，包括一些物理上现实的模型，这些模型否则会被标记为数学上不安全。我们还开发了证明演算以帮助验证PHS。
英文摘要：
Some hybrid systems models are unsafe for mathematically correct but physically unrealistic reasons. For example, mathematical models can classify a system as being unsafe on a set that is too small to have physical importance. In particular, differences in measure zero sets in models of cyber-physical systems (CPS) have significant mathematical impact on the mathematical safety of these models even though differences on measure zero sets have no tangible physical effect in a real system. We develop the concept of "physical hybrid systems" (PHS) to help reunite mathematical models with physical reality. We modify a hybrid systems logic (differential temporal dynamic logic) by adding a first-class operator to elide distinctions on measure zero sets of time within CPS models. This approach facilitates modeling since it admits the verification of a wider class of models, including some physically realistic models that would otherwise be classified as mathematically unsafe. We also develop a proof calculus to help with the verification of PHS.
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