Analysis of Time- versus Event-Triggered Consensus for a Single-Integrator Multi-Agent System

TL;DR

This paper analytically compares time- and event-triggered control schemes in a multi-agent consensus system, revealing that event-triggered control performs worse than time-triggered control as the number of agents increases.

Contribution

It provides the first analytical performance comparison of triggering schemes in multi-agent systems, highlighting differences from non-cooperative scenarios.

Findings

Event-triggered control performs worse than time-triggered control beyond a certain number of agents.

The paper derives the asymptotic order of the performance measure relative to the number of agents.

Performance differences depend on the number of agents, with event-triggered control degrading as agents increase.

Abstract

It is well known that the employed triggering scheme has great impact on the control performance when control loops operate under scarce communication resources. Various practical and simulative works have demonstrated the potential of event-triggered control to reduce communication while providing a similar performance level when compared to time-triggered control. For non-cooperative networked control systems, analytical performance comparisons of time- and event-triggered control support this finding under certain assumptions. While being well-studied in the non-cooperative setting, it remains unclear if and how the performance relationship of the triggering schemes is altered in a multi-agent system setup. To close this gap, in this paper, we consider a homogeneous single-integrator multi-agent consensus problem for which we compare the performance of time- and event-triggered control schemes analytically. Under the assumption of equal average triggering rates, we use the long-term average of the quadratic deviation from consensus as a performance measure to contrast the triggering schemes. Contrary to the non-cooperative setting, we prove that event-triggered control performs worse than time-triggered control beyond a certain number of agents in this setup. In addition, we derive the asymptotic order of the performance measure as a function of the number of agents under both triggering schemes.