[Paper Review] Distributed event-triggered coordination for average consensus on weight-balanced digraphs

Cameron Nowzari, Jorge Cortés|arXiv (Cornell University)|Jul 29, 2014

Distributed Control Multi-Agent Systems4 citations

TL;DR

This paper proposes a distributed event-triggered algorithm for multi-agent average consensus on weight-balanced digraphs, enabling agents to update communication and control based on local state events without continuous neighbor monitoring. It guarantees exponential convergence to the initial average, excludes Zeno behavior, and requires no global parameter knowledge, with extensions to switching topologies and periodic implementations.

ABSTRACT

This paper proposes a novel distributed event-triggered algorithmic solution to the multi-agent average consensus problem for networks whose communication topology is described by weight-balanced, strongly connected digraphs. The proposed event-triggered communication and control strategy does not rely on individual agents having continuous or periodic access to information about the state of their neighbors. In addition, it does not require the agents to have a priori knowledge of any global parameter. We show that, under the proposed law, events cannot be triggered an infinite number of times in any finite period (i.e., no Zeno behavior), and that the resulting network executions provably converge to the average of the initial agents' states exponentially fast. We also provide weaker conditions on connectivity under which convergence is guaranteed when the communication topology is switching. Simulations illustrate our results.

Motivation & Objective

• To address the inefficiency of continuous or periodic communication in multi-agent average consensus by designing a distributed event-triggered strategy.
• To enable agents to operate without continuous access to neighbor states or knowledge of global network parameters.
• To ensure Zeno-free execution and exponential convergence on weight-balanced digraphs, including switching topologies.
• To develop a periodic implementation that avoids continuous triggering function evaluation.
• To extend prior work from undirected to general weight-balanced directed graphs with provable convergence guarantees.

Proposed method

• The algorithm uses state-dependent event triggers based on local estimation errors, enabling agents to decide when to communicate or update control based on local conditions.
• A Lyapunov function is constructed to prove exponential convergence to the average of initial states under the event-triggered law.
• The design ensures inter-event times are bounded away from zero, preventing Zeno behavior, via a lower bound on the minimum inter-event time.
• For switching topologies, convergence is proven under weak connectivity assumptions, such as jointly strongly connected or uniformly jointly balanced digraphs.
• A periodic implementation is introduced where triggering functions are evaluated only at sampling instants, reducing computational load.
• The periodic variant uses a sufficient condition on the sampling period to guarantee asymptotic correctness, with trade-offs between communication and convergence rate controlled by a design parameter σ.

Experimental results

Research questions

• RQ1 Can event-triggered communication and control be designed for average consensus on weight-balanced digraphs without requiring continuous neighbor state access?
• RQ2 Does the proposed algorithm avoid Zeno behavior, ensuring finite events in finite time intervals?
• RQ3 Can exponential convergence to the initial average be guaranteed under the event-triggered law without global parameter knowledge?
• RQ4 How does the algorithm perform under switching communication topologies, and what weaker connectivity conditions suffice?
• RQ5 Can a periodic implementation be designed that maintains correctness while reducing continuous evaluation of triggering conditions?

Key findings

• The proposed event-triggered algorithm achieves exponential convergence to the average of initial agent states on weight-balanced digraphs without requiring continuous neighbor state monitoring.
• The algorithm excludes Zeno behavior, with a positive lower bound on inter-event times, ensuring no infinite triggering in finite time.
• Convergence is guaranteed under switching topologies if the union of the graphs over time intervals is jointly strongly connected or uniformly jointly weight-balanced.
• A periodic implementation of the algorithm is proposed, where triggering functions are evaluated only at discrete sampling times, reducing computational cost.
• Simulations show a trade-off between communication frequency and convergence speed: higher σ values reduce communication but slow convergence.
• The periodic variant maintains asymptotic correctness when the sampling period satisfies a sufficient condition derived from the system's dynamics and network structure.