Active Secure Neighbor Selection in Multi-Agent Systems with Byzantine Attacks

TL;DR

The paper addresses resilient consensus in multi-agent systems facing Byzantine adversaries by introducing an active secure neighbor selection (ASNS) framework. It leverages a pre-discriminative graph to define candidate neighbor sets and actively selects a minimal, secure subset of in-neighbors to form a directed spanning tree among the normal agents, without requiring initial connectivity. The approach reduces communication overhead and relaxes robustness requirements (achieving resilience with ${p\le F+1}$), while enabling dynamic topology reconstruction when attacks shift targets. Numerical results illustrate that ASNS can outperform existing detectors and MSR-based methods, particularly on graphs with limited connectivity, demonstrating practical robustness and efficiency in adversarial environments.

Abstract

This paper investigates the problem of resilient control for multi-agent systems in the presence of Byzantine adversaries via an active secure neighbor selection framework. A pre-discriminative graph is first constructed to characterize the admissible set of candidate neighbors for each agent. Based on this graph, a dynamic in-neighbor selection strategy is proposed, wherein each agent actively selects a subset of its pre-discriminative neighbors. The number of selected neighbors is adjustable, allowing for a trade-off between communication overhead and robustness, with the minimal case requiring only a single in-neighbor. The proposed strategy facilitates the reconstruction of a directed spanning tree among normal agents following the detection and isolation of Byzantine agents. It achieves resilient consensus without imposing any assumptions on the initial connectivity among normal agents. Moreover, the approach significantly reduces communication burden while maintaining resilience to adversarial behavior. A numerical example is provided to illustrate the effectiveness of the proposed method.

Figures (10)

• Figure 1: (a) $\mathcal{G}(k-1)$: the communication graph corresponding to time $k-1$ under attacks occurring at time $k$; (b) $\mathcal{G}_{pre}(k)$: the pre-discriminative graph at time $k$ ; (c) $\mathcal{G}(k)$: the communication graph at time $k$ after the ASNS strategy with $\mathcal{G}(k)\subseteq \mathcal{G}_{pre}(k)$.
• Figure 2: (a) $\mathcal{G}_{\mathcal{A}\text{-}pre}(k)$: the subgraph of agents in ${\mathcal{A}}(0,k)$ corresponding to $\mathcal{G}_{pre}(k)$ in Fig. \ref{['GOfig9qqqq90']}(b); (b) $\mathcal{G}_{\mathcal{A}}(k)$: the subgraph of agents in ${\mathcal{A}}(0,k)$ corresponding to $\mathcal{G}(k)$ in Fig. \ref{['GOfig9qqqq90']}(c) with $\mathcal{G} _{\mathcal{A}}(k)\subseteq \mathcal{G} _{\mathcal{A}\text{-}pre}(k)$.
• Figure 3: Pre-Discriminative Graph $\mathcal{G}_{pre}(k)$ Construction Strategy
• Figure 4: Active Secure Neighbor Selection Strategy for Flexible Communication
• Figure 5: (a) The initial communication graph ${\mathcal{G}}(0)$; (b) The initial pre-discriminative graph $\mathcal{G}_{pre}(0)$.

Theorems & Definitions (19)

• Definition 1
• Remark 1
• Definition 2
• Definition 3
• Remark 2
• Proposition 1
• Lemma 1
• proof
• Proposition 2
• proof