Abstracting the Sampling Behaviour of Stochastic Linear Periodic Event-Triggered Control Systems

TL;DR

This paper develops a framework using Interval Markov Chains to analyze the sampling behavior of stochastic linear periodic event-triggered control systems, enabling prediction and understanding of their sampling patterns.

Contribution

It introduces a novel abstraction method for stochastic ETC systems using IMCs, extending previous non-stochastic approaches and providing a generic framework for sampling analysis.

Findings

Bounded expected values of sampling functions are computed using IMCs.

The framework is extendable to various sampling indicators.

Provides a generic approach for analyzing stochastic ETC sampling patterns.

Abstract

Recently, there have been efforts towards understanding the sampling behaviour of event-triggered control (ETC), for obtaining metrics on its sampling performance and predicting its sampling patterns. Finite-state abstractions, capturing the sampling behaviour of ETC systems, have proven promising in this respect. So far, such abstractions have been constructed for non-stochastic systems. Here, inspired by this framework, we abstract the sampling behaviour of stochastic narrow-sense linear periodic ETC (PETC) systems via Interval Markov Chains (IMCs). Particularly, we define functions over sequences of state-measurements and interevent times that can be expressed as discounted cumulative sums of rewards, and compute bounds on their expected values by constructing appropriate IMCs and equipping them with suitable rewards. Finally, we argue that our results are extendable to more general forms of functions, thus providing a generic framework to define and study various ETC sampling indicators.