Resistant Topology Inference in Consensus Networks: A Feedback-Based Design

TL;DR

This paper addresses privacy risks in deterministic consensus networks by designing feedback-based controls to resist topology inference without disrupting consensus. It introduces an accurate-inference criterion combining solvability and deviation, and develops an invariant-subspace framework to study when topology estimators become unsolvable or inaccurate. A Laplacian-structure distributed design is proposed to achieve resistance while preserving convergence, with theoretical guarantees and numerical validation. The results enhance privacy in distributed coordination applications and suggest avenues for extending resistant designs to broader network dynamics.

Abstract

Consensus networks are widely deployed in numerous civil and industrial applications. However, the process of reaching a common consensus among nodes can unintentionally reveal the network's topology to external observers by appropriate inference techniques. This paper investigates a feedback-based resistant inference design to prevent the topology from being inferred using data, while preserving the original consensus convergence. First, we characterize the conditions to preserve the original consensus, and introduce the ''accurate inference'' notion, which accounts for both the uniqueness of the solution to topology inference (solvability) and the deviation from the original topology (accuracy). Then, we employ invariant subspace analysis to characterize the solvability. Even when unique inference remains possible, we provide necessary and sufficient conditions for the feedback design to induce inaccurate inference, and give a Laplacian structure based distributed design. Simulations validate the effectiveness of the method.

Figures (1)

• Figure 1: State convergence error and inference performance under $\tilde{W}$

Theorems & Definitions (16)

• Definition 1
• Lemma 1
• proof
• Theorem 1
• proof
• Definition 2
• Lemma 2
• Lemma 3
• proof
• Theorem 2