Abstract Cyber–physical Systems (CPS) involve a network of discrete controllers that control physical processes, e.g., pacemakers controlling the heart rhythm. The intuitive and formal Hybrid Automata (HA) based modelling approach for CPS is gaining momentum. HA combines the model of the plant along with its discrete controller resulting in a piece-wise continuous system with discontinuities. Accurate detection of these discontinuities, using appropriate level crossing detectors, is a key challenge to simulation of CPS modelled in HA. Existing techniques employ time discrete numerical integration with bracketing for level crossing detection. These techniques involve back-tracking and are highly non-deterministic and hence error prone. As level crossings happen based on the values of continuous variables, Quantized State System (QSS)-integration may be more suitable. We propose a dynamic quanta based execution framework for HA. A CPS modelled as a HA is first translated into the proposed formal intermediate format called the Quantized State Hybrid Automata (QSHA). The QSHA is then executed using a discrete event simulation algorithm based on quantized state semantics. The developed formal model and the associated simulation framework guarantees that: ① all level crossings are accurately detected and ② the time of the level crossing is also accurate within floating point error bounds. Interestingly, benchmark results reveal that the proposed simulation technique takes 720, 2.17, 1.33 and 4.41 times fewer simulation steps compared to QSS-1, QSS-3, Runge–Kutta (RK)-45, and Differential Algebraic System Solver (DASSL) integration based techniques, respectively.

中文翻译：

---

混合自动机的动态量化状态系统执行框架

摘要 信息物理系统 (CPS) 涉及控制物理过程的离散控制器网络，例如控制心律的起搏器。直观和正式的基于混合自动机 (HA) 的 CPS 建模方法正在获得动力。HA 将工厂模型与其离散控制器相结合，从而形成具有不连续性的分段连续系统。使用适当的水平交叉检测器准确检测这些不连续性是在 HA 中模拟 CPS 的关键挑战。现有技术采用带有包围的时间离散数值积分来进行平交道口检测。这些技术涉及回溯，并且是高度不确定的，因此容易出错。当基于连续变量的值发生水平交叉时，量化状态系统 (QSS) 集成可能更合适。我们为 HA 提出了一个基于动态量子的执行框架。建模为 HA 的 CPS 首先被转换为提议的正式中间格式，称为量化状态混合自动机 (QSHA)。然后使用基于量化状态语义的离散事件模拟算法执行 QSHA。开发的形式模型和相关的仿真框架保证：①所有平交路口都被准确检测，②平交路口的时间也在浮点误差范围内准确。有趣的是，基准测试结果表明，与 QSS-1、QSS-3、Runge-Kutta (RK)-45 和微分代数系统求解器 (DASSL) 集成相比，所提出的仿真技术所需的仿真步骤少了 720、2.17、1.33 和 4.41 倍基于技术，