Abstract In this paper, we introduce and characterize the notion of approximate predictability for the general class of pseudo-metric systems, which are a powerful modeling framework to deal with complex heterogeneous systems such as hybrid systems. Approximate predictability corresponds to the possibility of predicting the occurrence of specific states belonging to a particular subset of interest, in advance with respect to their occurrence, on the basis of observations. We establish a relation between approximate predictability of a given pseudo-metric system and approximate predictability of a pseudo-metric system that approximately simulates the given one. This relation allows checking approximate predictability of a system with an infinite number of states, provided that one is able to construct a pseudo-metric system with a finite number of states and inputs, approximating the original one in the sense of approximate simulation. To demonstrate the usefulness of our results, we apply them to the analysis of approximate predictability of Piecewise Affine (PWA) systems, a well studied class of hybrid systems for which, however, to the best of our knowledge, there are no results available in the current literature on predictability. An illustrative example is also included, which demonstrates the applicability of our results.

中文翻译：

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伪度量系统的近似可预测性

摘要 在本文中，我们介绍并描述了一般类伪度量系统的近似可预测性概念，这是处理复杂异构系统（如混合系统）的强大建模框架。近似可预测性对应于基于观察提前预测属于特定感兴趣子集的特定状态的发生的可能性。我们建立了给定伪度量系统的近似可预测性和近似模拟给定系统的伪度量系统的近似可预测性之间的关系。这种关系允许检查具有无限多个状态的系统的近似可预测性，前提是能够构建一个具有有限数量状态和输入的伪度量系统，在近似模拟的意义上逼近原始系统。为了证明我们的结果的有用性，我们将它们应用于分段仿射 (PWA) 系统的近似可预测性分析，这是一类经过充分研究的混合系统，然而，据我们所知，在当前关于可预测性的文献。还包括一个说明性示例，它证明了我们结果的适用性。然而，据我们所知，当前的文献中没有关于可预测性的结果。还包括一个说明性示例，它证明了我们结果的适用性。然而，据我们所知，当前的文献中没有关于可预测性的结果。还包括一个说明性示例，它证明了我们结果的适用性。