Chaos and Order in Event-Triggered Control

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Abstract

Event-triggered control (ETC) is claimed to provide significant reductions in sampling frequency when compared to periodic sampling, but little is formally known about its generated traffic. This work shows that ETC can exhibit very complex, even chaotic traffic, especially when the triggering condition is aggressive in reducing communications. First, by looking at the map dictating the evolution of states sampled, we characterize limit traffic patterns by observing invariant lines and planes through the origin, as well as their attractivity. Then, we present abstraction-based methods to compute limit metrics, such as limit average and limit inferior inter-sample time (IST) of periodic ETC (PETC), with considerations to the robustness of such metrics, as well as measuring the emergence of chaos. The methodology and tools allow us to find ETC examples that provably outperform periodic sampling in terms of average IST. In particular for PETC, we prove that this requires aperiodic or chaotic traffic.

Original languageEnglish
Pages (from-to)6541-6556
JournalIEEE Transactions on Automatic Control
Volume68
Issue number11
DOIs
Publication statusPublished - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

  • Behavioral sciences
  • Chaotic communication
  • chaotic systems
  • computational methods
  • Event-triggered control
  • Extraterrestrial measurements
  • hybrid systems
  • Linear systems
  • Measurement
  • sampled-data control
  • Traffic control
  • Trajectory

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