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Consensus and Flocking under Communication Failure

Fabio Ancona, Mohamed Bentaibi, Francesco Rossi

TL;DR

This work studies consensus and flocking in cooperative multi-agent networks subject to communication failures modeled by time-varying weights $M_{ij}(t)$. It shows that either persistent excitation (PE) or integral scrambling coefficient (ISC) suffices for first-order consensus with explicit exponential rates, and that second-order flocking holds under a standard nonintegrability condition on the interaction function $\phi$, also under PE or ISC. A key methodological contribution is a real-line contraction analysis using barrier and Grönwall arguments, extended to $\mathbb{R}^d$ via a projection-based approach, complemented by explicit rate estimates for velocity convergence. Together, the results provide robust coordination guarantees under intermittent communications and quantify the residual performance gap through concrete convergence rates.

Abstract

For networked systems, Persistent Excitation and Integral Scrambling Condition are conditions ensuring that communication failures between agents can occur, but a minimal level of service is ensured. We consider cooperative multi-agent systems satisfying either of such conditions. For first-order systems, we prove that consensus is attained. For second-order systems, flocking is attained under a standard condition of nonintegrability of the interaction function. In both cases and under both conditions, the original goal is reached under no additional hypotheses on the system with respect to the case of no communication failures.

Consensus and Flocking under Communication Failure

TL;DR

This work studies consensus and flocking in cooperative multi-agent networks subject to communication failures modeled by time-varying weights . It shows that either persistent excitation (PE) or integral scrambling coefficient (ISC) suffices for first-order consensus with explicit exponential rates, and that second-order flocking holds under a standard nonintegrability condition on the interaction function , also under PE or ISC. A key methodological contribution is a real-line contraction analysis using barrier and Grönwall arguments, extended to via a projection-based approach, complemented by explicit rate estimates for velocity convergence. Together, the results provide robust coordination guarantees under intermittent communications and quantify the residual performance gap through concrete convergence rates.

Abstract

For networked systems, Persistent Excitation and Integral Scrambling Condition are conditions ensuring that communication failures between agents can occur, but a minimal level of service is ensured. We consider cooperative multi-agent systems satisfying either of such conditions. For first-order systems, we prove that consensus is attained. For second-order systems, flocking is attained under a standard condition of nonintegrability of the interaction function. In both cases and under both conditions, the original goal is reached under no additional hypotheses on the system with respect to the case of no communication failures.
Paper Structure (8 sections, 12 theorems, 58 equations)

This paper contains 8 sections, 12 theorems, 58 equations.

Table of Contents

  1. Models of opinion formation
  2. General properties
  3. Dynamics on the real line
  4. Proof of main results
  5. Proof of Theorem \ref{['t-consensus']} in $\mathbb{R}$
  6. Proof of Theorem \ref{['t-consensus']} in $\mathbb{R}^d$
  7. Proof of Theorem \ref{['t-flocking']}
  8. Conclusions and future directions

Key Result

Theorem 1

Let $\{x_i(t)\}_{i=1}^N$ be a solution of e-ODE with initial data $\{\bar{x}_i\}_{i=1}^N$. Assume the following conditions: Fix $T,\mu>0$ and assume that one of the following cases holds: either all $M_{ij}$ satisfy e-PE, or the family $\{M_{ij}\}_{i,j=1,\ldots,N}$ satisfies e-ISC. Then, there exists $\gamma>0$, which value is explicitly given in Proposition p-1st below, such that the following e

Theorems & Definitions (15)

  • Definition 1: Persistent excitation
  • Definition 2: Integral Scrambling Coefficient
  • Theorem 1
  • Theorem 2
  • Lemma 3
  • Lemma 4
  • Proposition 5
  • Lemma 6
  • Lemma 7
  • Proposition 8
  • ...and 5 more