Computing the sampling performance of event-triggered control

TL;DR

This paper introduces a method to estimate the minimum average inter-sample time in event-triggered control systems, providing insights into traffic patterns and resource usage in networked control systems.

Contribution

It develops a formal approach using bisimulation refinement to estimate and exactly determine the minimum average inter-sample time in PETC for linear systems.

Findings

Provides a lower bound for MAIST estimation.

Identifies conditions for exact MAIST calculation.

Enhances understanding of traffic behavior in ETC systems.

Abstract

In the context of networked control systems, event-triggered control (ETC) has emerged as a major topic due to its alleged resource usage reduction capabilities. However, this is mainly supported by numerical simulations, and very little is formally known about the traffic generated by ETC. This work devises a method to estimate, and in some cases to determine exactly, the minimum average inter-sample time (MAIST) generated by periodic event-triggered control (PETC) of linear systems. The method involves abstracting the traffic model using a bisimulation refinement algorithm and finding the cycle of minimum average length in the graph associated to it. This always gives a lower bound to the actual MAIST. Moreover, if this cycle turns out to be related to a periodic solution of the closed-loop PETC system, the performance metric is exact.