Abstract: Time Petri net can analyze not only the logic level system performance, but also the time-level system performance by the introduction of the time factor based on the proto-type Petri net. However, the generation of CPS (cyber-physical system) containing spatial factors increases the necessary further expansion to time Petri net. CPS integrates computing system and physical system. It has not only the ability of real-time perception to the physical environment, but also the ability of controlling the physical entities to change the physical environment. This paper analyzes the physical characteristics and properties of CPS and the location change process of physical entities in CPS in depth. Then it proposes a formal modeling method of physical entities in CPS, and constructs a spatio-temporal Petri net model by introducing space factor into the traditional time Petri net, which can describe not only the logic and time-level behavior of physical entities, but also the change of state caused by the position change of physical entities. At last an example of robot control system proves the effectiveness of spatio-temporal Petri net model.

Key words: time Petri net, cyber-physical system (CPS), physical entities, spatial information, spatio-temporal Petri net

摘要： 时间Petri网在经典Petri网的基础上引入了时间因素，不仅能分析逻辑层次的系统性能，还能分析时间层次的系统性能，然而包含空间因素的信息物理融合系统（cyber-physical system，CPS）的产生需要对时间Petri网进行拓展。CPS集成计算系统和物理系统，不仅能够实时感知物理环境信息，并且能够通过物理实体改变物理环境。对CPS的物理层面特点进行了深入分析，研究了CPS物理实体的属性及其位置变迁过程，提出了一种CPS物理实体的形式化建模方法。在时间Petri网的基础上引入了空间因素，构造了时空Petri网模型，使其不仅能够描述物理实体逻辑及时间层次的行为，并且能够描述物理实体位置变迁所引起的状态变化。最后以机器人控制系统为例，进一步阐述了时空Petri网模型的有效性。

关键词: 时间Petri网, 信息物理融合系统（CPS）, 物理实体, 空间信息, 时空Petri网