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Average Consensus over Directed Networks in Open Multi-Agent Systems with Acknowledgement Feedback

Evagoras Makridis, Andreas Grammenos, Gabriele Oliva, Evangelia Kalyvianaki, Christoforos N. Hadjicostis, Themistoklis Charalambous

TL;DR

This paper introduces a novel ratio consensus algorithm (OPENRC) based on acknowledgement feedback, designed to be robust to agent arrivals and departures, as well as to unbalanced directed network topologies, and proves the convergence of the OpenRC algorithm using column-stochasticity and masspreservation properties.

Abstract

In this paper, we address the distributed average consensus problem over directed networks in open multi-agent systems (OMAS), where the stability of the network is disrupted by frequent agent arrivals and departures, leading to a time-varying average consensus target. To tackle this challenge, we introduce a novel ratio consensus algorithm (OPENRC) based on acknowledgement feedback, designed to be robust to agent arrivals and departures, as well as to unbalanced directed network topologies. We demonstrate that when all active agents execute the OPENRC algorithm, the sum of their state variables remains constant during quiescent epochs when the network remains unchanged. By assuming eventual convergence during such quiescent periods following persistent variations in system composition and size, we prove the convergence of the OPENRC algorithm using column-stochasticity and mass-preservation properties. Finally, we apply and evaluate our proposed algorithm in a simulated environment, where agents are departing from and arriving in the network to highlight its resilience against changes in the network size and topology.

Average Consensus over Directed Networks in Open Multi-Agent Systems with Acknowledgement Feedback

TL;DR

This paper introduces a novel ratio consensus algorithm (OPENRC) based on acknowledgement feedback, designed to be robust to agent arrivals and departures, as well as to unbalanced directed network topologies, and proves the convergence of the OpenRC algorithm using column-stochasticity and masspreservation properties.

Abstract

In this paper, we address the distributed average consensus problem over directed networks in open multi-agent systems (OMAS), where the stability of the network is disrupted by frequent agent arrivals and departures, leading to a time-varying average consensus target. To tackle this challenge, we introduce a novel ratio consensus algorithm (OPENRC) based on acknowledgement feedback, designed to be robust to agent arrivals and departures, as well as to unbalanced directed network topologies. We demonstrate that when all active agents execute the OPENRC algorithm, the sum of their state variables remains constant during quiescent epochs when the network remains unchanged. By assuming eventual convergence during such quiescent periods following persistent variations in system composition and size, we prove the convergence of the OPENRC algorithm using column-stochasticity and mass-preservation properties. Finally, we apply and evaluate our proposed algorithm in a simulated environment, where agents are departing from and arriving in the network to highlight its resilience against changes in the network size and topology.
Paper Structure (9 sections, 2 theorems, 21 equations, 5 figures, 1 algorithm)

This paper contains 9 sections, 2 theorems, 21 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Setting
  3. Open Network Model
  4. Assumptions
  5. Problem Statement
  6. OpenRC Algorithm
  7. Eventual Correctness Analysis
  8. Numerical Examples
  9. Conclusions

Key Result

Theorem 1

Let Assumptions ass:1 and ass:2 hold true. Then, the following holds for all $k\geq 0$:

Figures (5)

  • Figure 1: OMAS with directional information flow. The size of the network changes as time progresses with agents joining the network, and present ones departing from the network.
  • Figure 2: Weight assignment of node $v_j \in \mathcal{D}(k)$. Nodes denoted in light blue belong in $\mathcal{R}(k)$, while the ones denoted in light red belong in $\mathcal{D}(k)$.
  • Figure 3: Weight assignment of node $v_j \in \mathcal{R}(k)$. Nodes denoted in light blue belong in $\mathcal{R}(k)$, while the ones denoted in light red belong in $\mathcal{D}(k)$.
  • Figure 4: Evolution with time $k$, of the active agents' ratios $z_i(k)$ using the OpenRC algorithm.
  • Figure 5: The average consensus error, $e(k) = \Vert \mathop{\mathrm{diag}}({\boldsymbol{\alpha}(k)}) \boldsymbol{z}(k) - \mathbf{1}\bar{x}(k)\Vert_2$, (upper); the number of active agents, $n(k)$, (lower), with time $k$.

Theorems & Definitions (5)

  • Remark 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof