[论文解读] Consensus Computation in Unreliable Networks: A System Theoretic Approach

Fabio Pasqualetti, Antonio Bicchi+1 more|arXiv (Cornell University)|Jul 16, 2010

Distributed systems and fault tolerance参考文献 24被引用 4

一句话总结

该论文提出了一种基于系统理论的框架，通过未知输入估计检测并识别线性一致性网络中故障或恶意代理。研究证明，为实现对 $k$ 个拜占庭代理的通用检测与识别，网络需具备 $2k+1$-连通性；而对于 $k$ 个故障代理，$k+1$-连通性已足够，从而在对抗性行为下仍能实现鲁棒一致性。

ABSTRACT

This work addresses the problem of ensuring trustworthy computation in a linear consensus network. A solution to this problem is relevant for several tasks in multi-agent systems including motion coordination, clock synchronization, and cooperative estimation. In a linear consensus network, we allow for the presence of misbehaving agents, whose behavior deviate from the nominal consensus evolution. We model misbehaviors as unknown and unmeasurable inputs affecting the network, and we cast the misbehavior detection and identification problem into an unknown-input system theoretic framework. We consider two extreme cases of misbehaving agents, namely faulty (non-colluding) and malicious (Byzantine) agents. First, we characterize the set of inputs that allow misbehaving agents to affect the consensus network while remaining undetected and/or unidentified from certain observing agents. Second, we provide worst-case bounds for the number of concurrent faulty or malicious agents that can be detected and identified. Precisely, the consensus network needs to be 2k+1 (resp. k+1) connected for k malicious (resp. faulty) agents to be generically detectable and identifiable by every well behaving agent. Third, we quantify the effect of undetectable inputs on the final consensus value. Fourth, we design three algorithms to detect and identify misbehaving agents. The first and the second algorithm apply fault detection techniques, and affords complete detection and identification if global knowledge of the network is available to each agent, at a high computational cost. The third algorithm is designed to exploit the presence in the network of weakly interconnected subparts, and provides local detection and identification of misbehaving agents whose behavior deviates more than a threshold, which is quantified in terms of the interconnection structure.

研究动机与目标

• 解决在存在行为异常代理的不可靠多智能体网络中，确保可信一致性计算的挑战。
• 将异常行为建模为影响网络动态的未知、不可测量输入。
• 刻画在某些观察者视角下，异常代理可能保持不可检测或无法识别的条件。
• 为检测和识别故障与恶意代理提供基于连通性的鲁棒性边界。
• 设计在计算与拓扑约束下可扩展、分布式的本地检测与识别算法。

提出的方法

• 在未知输入系统理论框架内，形式化异常行为检测与识别问题。
• 利用残差生成与分析，检测与正常一致性行为的偏差。
• 基于残差的无穷范数，定义一种基于阈值的识别方案，以区分异常代理。
• 利用网络聚类与弱连接结构，实现在无需全局拓扑知识条件下的本地检测。
• 应用具有全局知识的故障检测技术，以实现完整检测与识别，但计算成本较高。
• 推导不可检测输入的最坏情况边界，并量化其对最终一致性值的影响。

实验结果

研究问题

• RQ1 在何种网络连通性条件下，能够确保线性一致性网络中 $k$ 个恶意代理的通用可检测性与可识别性？
• RQ2 不可检测输入如何影响最终的一致性值？其结构约束是什么？
• RQ3 能否仅使用本地信息与有限计算资源，检测并识别异常代理？
• RQ4 异常输入的增益与远程代理处其影响可观测性之间存在何种关系？
• RQ5 网络聚类如何影响本地检测与识别算法的性能？

主要发现

• 为使 $k$ 个恶意代理能被每个正常行为代理通用检测与识别，网络必须具备 $2k+1$-连通性。
• 对于 $k$ 个故障（不共谋）代理，$k+1$-连通性已足够实现通用检测与识别。
• 当 $\varepsilon \leq 0.01$ 时，本地识别方法在弱簇间连接的聚类网络中能正确检测并识别异常代理。
• 当 $\varepsilon = 0.01$ 时，阈值 $T = 0.1$ 可使代理 1 正确识别代理 2 为异常，依据是残差范数。
• 若 $\varepsilon = 0.03$，异常代理可能因残差幅值与正常代理重叠而保持不可检测。
• 所提出的本地算法在大规模聚类网络中表现良好，且随着簇间边权重 $\varepsilon$ 的减小，性能持续提升。