When Every Transmission Counts: Event-Trigger Threshold Regulation for STL Properties

We propose a novel event-trigger threshold (ETT) regulation mechanism <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ETT</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sup> based on Signal Temporal Logic (STL) properties significantly extending recent work on ETT regulation for Propositional Logic properties. We utilize the quantitative semantics of STL to construct a method for computing and merging suitable ETTs for different requirements in complex STL specifications. Contrary to related work on event-triggered control for STL properties, we apply the event-triggering logic to the measured signals individually rather than the control output and assume that an existing periodic controller is defined. By exploiting the early satisfaction detection capabilities of STL and analyzing the property structure, our method aims to reduce the number of triggered events, while maintaining satisfaction of system properties. To evaluate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ETT</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sup>, we consider a simulated adaptive cruise control case-study where STL is used to encode complex safety and performance properties and the ETTs of measured signals are regulated accordingly. We test three different properties in two different scenarios to showcase how STL and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ETT</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ρ</sup> can identify intricate circumstances where it is possible to significantly reduce the number of triggered events relative to a constant ETT.