Extending Signal Temporal Logic with Quantitative Semantics by Intervals for Robust Monitoring of Cyber-physical Systems

Monitoring is the core procedure of runtime verification of cyber-physical systems (CPS) and provides an evaluation of a signal with respect to a given specification. For formally specifying requirements with time constraints for CPS, Signal Temporal Logic (STL) is a well-known specification language with powerful semantics. However, with existing semantics of STL it is not feasible to monitor signals with spatial deviation and time delay. Therefore, we introduce STL with Quantitative Interval Semantics to solve this problem. Based on this newly developed semantics, we derived an algorithm called RoMoTeS (Robust Monitoring for Temporal Specifications) to monitor a signal with finite length with respect to an STL formula. It provides a real-valued interval for every point in time, which contains all possible signed distances between the deviation polytope determined by the measured data point (exposed to deviation and delay) and the permissive space specified by an STL specification. Furthermore, it is proven that no satisfaction is reported when the signal is potentially falsifying such a specification. Finally, an automatic transmission controller model was used as a case study to show the applicability and usefulness of the proposed algorithm.