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Multi-Agent Resilient Consensus under Intermittent Faulty and Malicious Transmissions (Extended Version)

Sarper Aydın, Orhan Eren Akgün, Stephanie Gil, Angelia Nedić

TL;DR

This work tackles resilient consensus in a multi-agent network where legitimate and malicious agents share values over an undirected graph, focusing on intermittent faulty or malicious transmissions. It introduces a trust-based detection mechanism that uses time-varying thresholds and stochastic trust observations $\alpha_{ij}(t)\in[0,1]$ to construct a trusted neighborhood and weights, ensuring legitimate agents converge almost surely to a common value despite adversarial influence. The analysis proves geometric decay of misclassification probabilities, random finite-time stabilization of the trusted topology, and provides explicit probabilistic bounds on the deviation from the nominal consensus value, quantified by $\Delta_{\max}(T_0,\delta)$, which depend on network size, trust gaps, and growth rate parameters $\xi$ and $\gamma$. Numerical experiments corroborate the theoretical results, showing convergence and illustrating how attack probability $p_m$ and attack mode (consistent vs intermittent) affect convergence behavior and deviation. The approach offers a practical pathway for resilient distributed decision-making in cyber-physical systems by leveraging physical-layer trust observations alongside adaptive neighbor learning.

Abstract

In this work, we consider the consensus problem in which legitimate agents share their values over an undirected communication network in the presence of malicious or faulty agents. Different from the previous works, we characterize the conditions that generalize to several scenarios such as intermittent faulty or malicious transmissions, based on trust observations. As the standard trust aggregation approach based on a constant threshold fails to distinguish intermittent malicious/faulty activity, we propose a new detection algorithm utilizing time-varying thresholds and the random trust values available to legitimate agents. Under these conditions, legitimate agents almost surely determine their trusted neighborhood correctly with geometrically decaying misclassification probabilities. We further prove that the consensus process converges almost surely even in the presence of malicious agents. We also derive the probabilistic bounds on the deviation from the nominal consensus value that would have been achieved with no malicious agents in the system. Numerical results verify the convergence among agents and exemplify the deviation under different scenarios.

Multi-Agent Resilient Consensus under Intermittent Faulty and Malicious Transmissions (Extended Version)

TL;DR

This work tackles resilient consensus in a multi-agent network where legitimate and malicious agents share values over an undirected graph, focusing on intermittent faulty or malicious transmissions. It introduces a trust-based detection mechanism that uses time-varying thresholds and stochastic trust observations to construct a trusted neighborhood and weights, ensuring legitimate agents converge almost surely to a common value despite adversarial influence. The analysis proves geometric decay of misclassification probabilities, random finite-time stabilization of the trusted topology, and provides explicit probabilistic bounds on the deviation from the nominal consensus value, quantified by , which depend on network size, trust gaps, and growth rate parameters and . Numerical experiments corroborate the theoretical results, showing convergence and illustrating how attack probability and attack mode (consistent vs intermittent) affect convergence behavior and deviation. The approach offers a practical pathway for resilient distributed decision-making in cyber-physical systems by leveraging physical-layer trust observations alongside adaptive neighbor learning.

Abstract

In this work, we consider the consensus problem in which legitimate agents share their values over an undirected communication network in the presence of malicious or faulty agents. Different from the previous works, we characterize the conditions that generalize to several scenarios such as intermittent faulty or malicious transmissions, based on trust observations. As the standard trust aggregation approach based on a constant threshold fails to distinguish intermittent malicious/faulty activity, we propose a new detection algorithm utilizing time-varying thresholds and the random trust values available to legitimate agents. Under these conditions, legitimate agents almost surely determine their trusted neighborhood correctly with geometrically decaying misclassification probabilities. We further prove that the consensus process converges almost surely even in the presence of malicious agents. We also derive the probabilistic bounds on the deviation from the nominal consensus value that would have been achieved with no malicious agents in the system. Numerical results verify the convergence among agents and exemplify the deviation under different scenarios.
Paper Structure (11 sections, 10 theorems, 58 equations, 2 figures, 1 algorithm)

This paper contains 11 sections, 10 theorems, 58 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Consensus Dynamics with Failures and Attacks
  3. Notation
  4. Consensus in Presence of Untrustworthy Agents
  5. Trusted Neighborhood Learning
  6. Analysis of Consensus Dynamics
  7. Convergence of Consensus Dynamics
  8. Deviation from Consensus under Intermittent Failures and Attacks
  9. Numerical Studies
  10. Conclusion
  11. Acknowledgements

Key Result

Lemma 1

Suppose Assumption as_trust holds. Let $\xi>0$ and $\gamma \in (0.5,1)$ be the parameters defined in Algorithm alg_trust. Let $j$ be an arbitrary legitimate neighbor of a legitimate agent $i$, i.e., $j \in \mathcal{N}_i^{\mathcal{L}}$ for agent $i \in \mathcal{L}$. Then, the misclassification probab where $\lambda = \min_{m \in \mathcal{M}} (d-c_m)$.

Figures (2)

  • Figure 1: Misclassification examples for an agent $i$ with three legitimate neighbors with aggregate trust values $\beta_{ij_1}(t)$, $\beta_{ij_2}(t)$, $\beta_{ij_3}(t)$ and a malicious neighbor with aggregate trust value $\beta_{im}(t)$. The aggregate trust values are placed on a number line where values to the right are larger and values to the left are smaller. The green area inside the brackets indicates the trusted region $\xi_t$ from Algorithm \ref{['alg_trust_neig']}.
  • Figure 2: The maximal deviation of the legitimate agents from the nominal consensus value. Malicious input $\eta$ shows the maximum impact that malicious agents can have on the system.

Theorems & Definitions (20)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Lemma 5
  • proof
  • ...and 10 more