单调控制系统的完整抽象：从基于模型系统到数据驱动系统
Complete Abstractions of Monotone Control Systems: From Model-based to Data-Driven Systems
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中文总结 AI 辅助
本文提出近似强上交替模拟关系，为单调系统构建完整抽象对，可通过空间离散化参数调谐保守性差距，并将结果扩展至无需显式模型的数据驱动系统，通过仿真验证理论结果。
中文摘要 AI 辅助
本文介绍了近似强上交替模拟（ASUAS），这是一种针对迁移系统的新行为关系。基于该关系，我们为单调系统构建了上稀疏和下稀疏抽象，二者共同构成完整抽象对：针对上稀疏抽象合成的任意控制器均可被细化为原系统的控制器，而下稀疏抽象不存在控制器则意味着原系统不存在控制器。该方法的关键特性是可通过调整空间离散化参数，可证地调谐两个抽象之间的保守性差距。我们进一步将这些结果从基于模型的设定扩展到数据驱动系统，其中抽象直接由有限采样数据构建，无需显式系统模型。理论结果通过仿真得到验证。
英文摘要
In this paper, we introduce the approximate strong upper alternating simulation (ASUAS), a new behavioral relation for transition systems. Building on this relation, we construct upper- and lower-sparse abstractions for monotone systems that together form a complete abstraction pair: any controller synthesized for the upper-sparse abstraction can be refined into a controller for the original system, and the absence of a controller for the lower-sparse abstraction implies the absence of a controller for the original system. A key feature of our approach is the ability to provably tune the conservativeness gap between the two abstractions by tuning the space-discretization parameter. We further extend these results, beyond the model-based setting, to data-driven systems, where the abstraction is constructed directly from finite sampled data, without requiring an explicit system model. The theoretical results are illustrated through simulations.
