Combining spatial and temporal primitives together is quite useful to specify dynamic behaviors of cyber-physical systems. The ability to represent spatio-temporal properties by means of formulas in spatio-temporal logics has recently found important applications in various fields, such as runtime verification, parameter synthesis, and falsification. In this paper, we present a spatio-temporal specification language, STSL, by combining signal temporal logic (STL) with a spatial logic \(\mathcal {S}4_{u}\) to characterize spatio-temporal dynamic behaviors of cyber-physical systems. This language is highly expressive: it allows the description of quantitative signals, by expressing spatio-temporal traces over real-valued signals in dense time, and Boolean signals, by constraining values of spatial objects across threshold predicates. STSL combines the power of temporal modalities and spatial operators and enjoys important properties such as safety and liveness. We provide the falsification problem through extending Lemire’s algorithm and a parameter synthesis procedure by calling the simulated annealing algorithm. We demonstrate the proposed approach on the adaptive cruise control system and path planning of quadrotors.

将空间和时间原语结合在一起对于指定网络物理系统的动态行为非常有用。通过时空逻辑中的公式来表示时空属性的能力最近在各个领域都有重要的应用，例如运行时验证、参数合成和证伪。在本文中，我们通过将信号时间逻辑 ( STL ) 与空间逻辑\(\mathcal {S}4_{u}\)相结合，提出了一种时空规范语言STSL表征网络物理系统的时空动态行为。这种语言具有很强的表现力：它允许通过在密集时间内表达实值信号的时空轨迹来描述定量信号，以及通过跨阈值谓词约束空间对象的值来描述布尔信号。STSL结合了时间模态和空间算子的力量，并享有安全性和活性等重要特性。我们通过调用模拟退火算法扩展 Lemire 算法和参数合成过程来提供证伪问题。我们在自适应巡航控制系统和四旋翼飞行器的路径规划上展示了所提出的方法。