This letter introduces a machine-learning approach to learning the semantic dynamics of correlated systems with different control rules and dynamics. By leveraging the Koopman operator in an autoencoder (AE) framework, the system's state evolution is linearized in the latent space using a dynamic semantic Koopman (DSK) model, capturing the baseline semantic dynamics. Signal temporal logic (STL) is incorporated through a logical semantic Koopman (LSK) model to encode system-specific control rules. These models form the proposed logical Koopman AE framework that reduces communication costs while improving state prediction accuracy and control performance, showing a 91.65% reduction in communication samples and significant performance gains in simulation.

翻译：本文提出一种机器学习方法，用于学习具有不同控制规则与动力学的相关系统的语义动态。通过将Koopman算子融入自编码器框架，系统状态演化在潜空间中被动态语义Koopman模型线性化，从而捕捉基础语义动态。信号时序逻辑通过逻辑语义Koopman模型进行整合，以编码系统特定的控制规则。这些模型共同构成了所提出的逻辑Koopman自编码器框架，该框架在提升状态预测精度与控制性能的同时显著降低了通信开销，仿真结果表明通信样本量减少91.65%，且各项性能指标均获得显著提升。