How improving performance may imply losing consistency in event-triggered consensus

TL;DR

This paper investigates how enhancing local information in event-triggered consensus control can improve performance but may lead to a loss of consistency, highlighting a trade-off in decentralized control schemes.

Contribution

It provides a novel analysis of the relationship between information richness, performance, and consistency in event-triggered consensus control with optimal inputs.

Findings

Enriching local information improves consensus performance.

Increased information can cause loss of consistency in event-triggered schemes.

Optimal control inputs are derived for different information and triggering scenarios.

Abstract

Event-triggered control is often argued to lower the average triggering rate compared to time-triggered control while still achieving a desired control goal, e.g., the same performance level. However, this property, often called consistency, cannot be taken for granted and can be hard to analyze in many settings. In particular, the performance properties of decentralized event-triggered control schemes with respect to time-triggered control remain mostly unexplored. Therefore, in this paper, we examine these performance properties for a consensus problem considering single-integrator agent dynamics, a level-triggering rule, and a complete communication graph. We consider the long-term average quadratic deviation from consensus as a performance measure. For this setting, we show that enriching the information the local controllers use improves the performance of the consensus algorithm but renders a previously consistent event-triggered control scheme inconsistent. In addition, we do so while deploying optimal control inputs which we derive for both information cases and triggering schemes. With this insight, we can furthermore explain the relationship between two seemingly contrasting consistency results from the literature.