Formal Analysis of the Sampling Behaviour of Stochastic Event-Triggered Control

TL;DR

This paper provides a formal analysis of the sampling behavior in stochastic event-triggered control systems by deriving bounds on key metrics using Markov chain abstractions, aiding performance prediction.

Contribution

It introduces a method to compute bounds on sampling metrics of stochastic PETC systems using Interval Markov Chains with reward structures, a novel formal approach.

Findings

Bounds on expected average intersampling time are computed.

Probability of maximum intersampling time triggering is estimated.

Numerical example demonstrates the effectiveness of the bounds.

Abstract

Analyzing Event-Triggered Control's (ETC) sampling behaviour is of paramount importance, as it enables formal assessment of its sampling performance and prediction of its sampling patterns. In this work, we formally analyze the sampling behaviour of stochastic linear periodic ETC (PETC) systems by computing bounds on associated metrics. Specifically, we consider functions over sequences of state measurements and intersampling times that can be expressed as average, multiplicative or cumulative rewards, and introduce their expectations as metrics on PETC's sampling behaviour. We compute bounds on these expectations, by constructing appropriate Interval Markov Chains equipped with suitable reward structures, that abstract stochastic PETC's sampling behaviour. Our results are illustrated on a numerical example, for which we compute bounds on the expected average intersampling time and on the probability of triggering with the maximum possible intersampling time in a finite horizon.