[Paper Review] Decentralized Event-Triggered Consensus over Unreliable Communication Networks

Eloy García, Yongcan Cao+1 more|arXiv (Cornell University)|Nov 24, 2015

Distributed Control Multi-Agent Systems28 references3 citations

TL;DR

This paper proposes a decentralized event-triggered consensus protocol for multi-agent systems over unreliable communication networks with non-consistent packet dropouts and time-varying delays. By enabling agents to autonomously trigger transmissions based on local error thresholds, the protocol ensures asymptotic consensus while avoiding Zeno behavior, even when packets are lost or delayed inconsistently across receivers.

ABSTRACT

This article studies distributed event-triggered consensus over unreliable communication channels. Communication is unreliable in the sense that the broadcast channel from one agent to its neighbors can drop the event-triggered packets of information, where the transmitting agent is unaware that the packet was not received and the receiving agents have no knowledge of the transmitted packet. Additionally, packets that successfully arrive at their destination may suffer from time-varying communication delays. In this paper, we consider directed graphs, and we also relax the consistency on the packet dropouts and the delays. Relaxing consistency means that the delays and dropouts for a packet broadcast by one agent can be different for each receiving node. We show that even under this challenging scenario, agents can reach consensus asymptotically while reducing transmissions of measurements based on the proposed event-triggered consensus protocol. In addition, positive inter-event times are obtained which guarantee that Zeno behavior does not occur.

Motivation & Objective

• To address the challenge of achieving consensus in multi-agent systems over unreliable communication networks where packet dropouts and delays are non-uniform across agents.
• To relax the assumption of consistent communication behavior—where all receivers experience the same dropout and delay—by allowing per-receiver variations.
• To design a decentralized event-triggered protocol that reduces transmission frequency while maintaining system stability and avoiding Zeno behavior.
• To establish sufficient conditions for asymptotic average consensus under general directed graphs with unreliable communication.

Proposed method

• Agents use local event-triggering rules based on measurement error thresholds, enabling autonomous transmission decisions without global synchronization.
• The protocol models communication failures as non-uniform packet dropouts and time-varying delays, where each receiving agent may experience different loss and delay patterns.
• A Lyapunov-based stability analysis is conducted using a modified error dynamics model that incorporates both measurement errors and delayed/lost updates.
• The inter-event time is bounded below using a derived inequality, ensuring non-Zeno behavior and guaranteeing a minimum time between transmissions.
• The consensus error is bounded using a matrix exponential decay estimate, with the bound depending on system parameters and delay bounds.
• A numerical example validates the theoretical results using a directed network of six agents with time-varying delays and stochastic packet loss.

Experimental results

Research questions

• RQ1 Can asymptotic consensus be achieved in multi-agent systems with decentralized event-triggered control under non-uniform packet dropouts and delays?
• RQ2 How can Zeno behavior be avoided in event-triggered consensus when communication is unreliable and inconsistent across receivers?
• RQ3 What are the sufficient conditions for average consensus in directed networks with unreliable communication and non-synchronized delays?
• RQ4 How does the choice of event-triggering threshold affect the minimum inter-event time and system robustness?
• RQ5 To what extent can transmission frequency be reduced while maintaining consensus under unreliable communication?

Key findings

• Asymptotic consensus is achieved under the proposed protocol even when packet dropouts and delays are non-consistent across receiving agents.
• The minimum inter-event time is bounded below by τ = 0.0025, ensuring that Zeno behavior does not occur.
• Admissible delays are bounded by d = 0.0223, which ensures stability and convergence under the given protocol parameters.
• The protocol maintains average consensus, as the initial average of agent states remains constant over time due to the undirected nature of the graph.
• Simulation results confirm convergence of all six agents to a common value despite intermittent packet losses and variable delays.
• The receiving time intervals are significantly longer than broadcasting intervals due to packet loss, confirming the impact of unreliable communication on update frequency.