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A Class of Distributed Event-Triggered Average Consensus Algorithms for Multi-Agent Systems

Ping Xu, Cameron Nowzari, Zhi Tian

TL;DR

A class of distributed event-triggered algorithms that solve the average consensus problem in multi-agent systems by designing events such that a specifically chosen Lyapunov function is monotonically decreasing to guarantee exponential convergence of the resulting system and exclusion of Zeno behaviours.

Abstract

This paper proposes a class of distributed event-triggered algorithms that solve the average consensus problem in multi-agent systems. By designing events such that a specifically chosen Lyapunov function is monotonically decreasing, event-triggered algorithms succeed in reducing communications among agents while still ensuring that the entire system converges to the desired state. However, depending on the chosen Lyapunov function the transient behaviors can be very different. Moreover, performance requirements also vary from application to application. Consequently, we are instead interested in considering a class of Lyapunov functions such that each Lyapunov function produces a different event-triggered coordination algorithm to solve the multi-agent average consensus problem. The proposed class of algorithms all guarantee exponential convergence of the resulting system and exclusion of Zeno behaviors. This allows us to easily implement different algorithms that all guarantee correctness to meet varying performance needs. We show that our findings can be applied to the practical clock synchronization problem in wireless sensor networks (WSNs) and further corroborate their effectiveness with simulation results.

A Class of Distributed Event-Triggered Average Consensus Algorithms for Multi-Agent Systems

TL;DR

A class of distributed event-triggered algorithms that solve the average consensus problem in multi-agent systems by designing events such that a specifically chosen Lyapunov function is monotonically decreasing to guarantee exponential convergence of the resulting system and exclusion of Zeno behaviours.

Abstract

This paper proposes a class of distributed event-triggered algorithms that solve the average consensus problem in multi-agent systems. By designing events such that a specifically chosen Lyapunov function is monotonically decreasing, event-triggered algorithms succeed in reducing communications among agents while still ensuring that the entire system converges to the desired state. However, depending on the chosen Lyapunov function the transient behaviors can be very different. Moreover, performance requirements also vary from application to application. Consequently, we are instead interested in considering a class of Lyapunov functions such that each Lyapunov function produces a different event-triggered coordination algorithm to solve the multi-agent average consensus problem. The proposed class of algorithms all guarantee exponential convergence of the resulting system and exclusion of Zeno behaviors. This allows us to easily implement different algorithms that all guarantee correctness to meet varying performance needs. We show that our findings can be applied to the practical clock synchronization problem in wireless sensor networks (WSNs) and further corroborate their effectiveness with simulation results.

Paper Structure

This paper contains 15 sections, 8 theorems, 47 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Statement
  4. Distributed Trigger Design
  5. Related work
  6. Proposed new algorithm
  7. Stability Analysis of Algorithm 2
  8. A Class of Event-Triggered Algorithms
  9. Case Study: Clock Synchronization
  10. Background
  11. Clock synchronization problem formulation
  12. Distributed event-triggered clock synchronization algorithms
  13. Simulation Results
  14. Conclusion
  15. Proof of Lemma \ref{['lemma:V2_dot_upbound']}

Key Result

Lemma 4.1

For $i \in \mathcal{V}$, with $b_i,c_j<\frac{1}{d_i^{out}}\; \forall i,j \in \mathcal{V}$, define $e_i(t)=\hat{x}_i(t)-x_i(t)$ as in Section subsec:related, with $u_i(t)$ given in eq:ctr_law_modified, then where

Figures (3)

  • Figure 1: Plots of the simulation results of the clock synchronization on Network 1. (a) The local clocks are the same for both algorithms. (b) Virtual clocks with the implementation of event-triggered control. Both Algorithm 1 (top) and Algorithm 2 (bottom) are able to synchronize the virtual clocks.
  • Figure 2: Plots of the triggering instances and the evolution of Lyapunov candidate functions on four networks when implementing both Algorithms. For figure (a), (c), (e), (g), Algorithm 1 is on the top and Algorithm 2 is on the bottom.
  • Figure 3: Plots of different evaluation metrics. For figure (a), (c), (e), (g), top: total events triggered, bottom: convergence time (bottom); for figure (b), (d), (f), (h), top: energy consumption, bottom: $H_2$-norm squared.

Theorems & Definitions (8)

  • Lemma 4.1
  • Corollary 4.2
  • Proposition 5.1
  • Theorem 5.2
  • Corollary 6.1
  • Lemma 7.1
  • Theorem 7.2
  • Theorem 7.3