Towards Traffic Bisimulation of Linear Periodic Event-Triggered Controllers

TL;DR

This paper introduces a method to create finite, exactly bisimilar models of linear systems under periodic event-triggered control, enabling precise prediction of event sequences and traffic analysis.

Contribution

It presents a novel approach to construct finite abstractions that are exactly bisimilar to linear PETC systems based on inter-event times.

Findings

Finite models can predict event sequences until a Lyapunov sublevel set.

Models enable computation of bounds on PETC average frequency.

Demonstrated effectiveness through a numerical case study.

Abstract

We provide a method to construct finite abstractions exactly bisimilar to linear systems under a modified periodic event-triggered control (PETC), when considering as output the inter-event times they generate. Assuming that the initial state lies on a known compact set, these finite-state models can exactly predict all sequences of sampling times until a specified Lyapunov sublevel set is reached. Based on these results, we provide a way to build tight models simulating the traffic of conventional PETC. These models allow computing tight bounds of the PETC average frequency and global exponential stability (GES) decay rate. Our results are demonstrated through a numerical case study.