标题： 基于未知模型和互连拓扑的无限网络的数据驱动安全证书 显示英文标题

标题： Data-Driven Safety Certificates of Infinite Networks with Unknown Models and Interconnection Topologies

摘要： 无限网络是由可数无限个子系统组成的复杂互联系统，由于网络看似无尽的互联特性（例如，统计道路上的车辆数量），精确计数存在重大挑战。 在这些情况下，网络中存在无限多个子系统，使得专为有限网络设计的现有分析框架无法适用于无限网络。 本文关注在组合框架内提供一种数据驱动的方法，用于具有未知数学模型和互连拓扑结构的无限网络的安全认证。 鉴于无限网络广泛维度带来的巨大计算复杂性，我们的方法利用了子系统的联合耗散性特性，这些特性由存储证书表征。 我们引入了创新的组合数据驱动条件，利用从数据中得出的未知子系统的存储证书，为无限网络构建一个屏障证书，同时在整个网络安全性上提供正确性保证。 我们证明了我们的组合数据驱动推理消除了检查传统耗散性条件的要求，而传统耗散性条件通常需要精确的互连拓扑知识。 此外，尽管现有的数据驱动文献表明样本复杂度随网络规模呈指数增长，我们展示了我们的组合策略显著将其降低到与子系统数量成线性比例。 我们在两个具有未知模型和互连拓扑结构的物理无限网络上展示了我们的数据驱动结果。 显示英文摘要

摘要： Infinite networks are complex interconnected systems comprising a countably infinite number of subsystems, where counting them precisely poses a significant challenge due to the seemingly endless interconnected nature of the network (e.g., counting vehicles on the road). In such scenarios, the presence of infinitely many subsystems within the network renders the existing analysis frameworks tailored for finite networks inapplicable to infinite ones. This paper is concerned with offering a data-driven approach, within a compositional framework, for the safety certification of infinite networks with both unknown mathematical models and interconnection topologies. Given the immense computational complexity stemming from the extensive dimension of infinite networks, our approach capitalizes on the joint dissipativity-type properties of subsystems, characterized by storage certificates. We introduce innovative compositional data-driven conditions to construct a barrier certificate for the infinite network leveraging storage certificates of its unknown subsystems derived from data, while offering correctness guarantees across the network safety. We demonstrate that our compositional data-driven reasoning eliminates the requirement for checking the traditional dissipativity condition, which typically mandates precise knowledge of the interconnection topology. In addition, while existing data-driven literature demonstrates an exponential trend in sample complexity with respect to network size, we showcase that our compositional strategy notably reduces it to a linear scale in terms of the number of subsystems. We illustrate our data-driven results on two physical infinite networks with unknown models and interconnection topologies.