[Paper Review] 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 tolerance24 references4 citations

TL;DR

This paper proposes a system-theoretic framework for detecting and identifying faulty or malicious agents in linear consensus networks using unknown-input estimation. It establishes that $2k+1$-connectivity is required for generic detection and identification of $k$ Byzantine agents, while $k+1$-connectivity suffices for $k$ faulty agents, enabling robust consensus even under adversarial behavior.

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.

Motivation & Objective

• Address the challenge of ensuring trustworthy consensus computation in unreliable multi-agent networks with misbehaving agents.
• Model misbehaviors as unknown, unmeasurable inputs affecting network dynamics.
• Characterize conditions under which misbehaving agents can remain undetected or unidentified from certain observers.
• Provide connectivity-based resilience bounds for detecting and identifying both faulty and malicious agents.
• Design scalable, distributed algorithms for local detection and identification under computational and topological constraints.

Proposed method

• Formulate the misbehavior detection and identification problem within an unknown-input system theory framework.
• Use residual generation and analysis to detect deviations from nominal consensus behavior.
• Define a threshold-based identification scheme using infinity-norm of residuals to distinguish misbehaving agents.
• Leverage network clustering and weak interconnections to enable local detection without global topology knowledge.
• Apply fault detection techniques with global knowledge for complete detection and identification at high computational cost.
• Derive worst-case bounds on undetectable inputs and quantify their impact on final consensus value.

Experimental results

Research questions

• RQ1 What network connectivity conditions ensure generic detectability and identifiability of $k$ malicious agents in a linear consensus network?
• RQ2 How do undetectable inputs affect the final consensus value, and what are their structural constraints?
• RQ3 Can misbehaving agents be detected and identified using only local information and limited computational resources?
• RQ4 What is the relationship between the gain of misbehaving inputs and the observability of their effects at remote agents?
• RQ5 How does network clustering influence the performance of local detection and identification algorithms?

Key findings

• For $k$ malicious agents to be generically detectable and identifiable by every well-behaving agent, the network must be $2k+1$-connected.
• For $k$ faulty (non-colluding) agents, $k+1$-connectivity is sufficient for generic detectability and identifiability.
• When $\varepsilon \leq 0.01$, the local identification method correctly detects and identifies misbehaving agents in clustered networks with weak inter-cluster connections.
• A threshold $T = 0.1$ enables agent 1 to correctly identify agent 2 as misbehaving when $\varepsilon = 0.01$, based on residual norms.
• If $\varepsilon = 0.03$, the misbehaving agent may remain undetected due to overlapping residual magnitudes with well-behaving agents.
• The proposed local algorithm performs well in large, clustered networks, with performance improving as inter-cluster edge weights $\varepsilon$ decrease.