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Privacy-Preserving Dynamic Average Consensus by Masking Reference Signals

Mihitha Maithripala, Zongli Lin

TL;DR

Privacy in dynamic average consensus is challenged by state exchanges revealing private signals x_i(t). We propose a masking-based DAC that uses per-edge random values to form zero-sum masks m_i and masked references x_{m,i}(t) = x_i(t) + m_i, enabling the standard DAC update to run without exposing private signals. Theoretical results show external eavesdroppers cannot recover x_i(t) and honest-but-curious agents cannot uniquely infer a neighbor's reference when at least one neighbor is legitimate, while the convergence rate remains unchanged due to the preserved Laplacian structure; simulations on a ring network validate both privacy guarantees and performance on par with conventional DAC. This approach achieves privacy with low overhead and without sacrificing tracking accuracy, making it suitable for secure distributed control and resource allocation in networks.

Abstract

In multi-agent systems, dynamic average consensus (DAC) is a decentralized estimation strategy in which a set of agents tracks the average of time-varying reference signals. Because DAC requires exchanging state information with neighbors, attackers may gain access to these states and infer private information. In this paper, we develop a privacy-preserving method that protects each agent's reference signal from external eavesdroppers and honest-but-curious agents while achieving the same convergence accuracy and convergence rate as conventional DAC. Our approach masks the reference signals by having each agent draw a random real number for each neighbor, exchanges that number over an encrypted channel at the initialization, and computes a masking value to form a masked reference. Then the agents run the conventional DAC algorithm using the masked references. Convergence and privacy analyses show that the proposed algorithm matches the convergence properties of conventional DAC while preserving the privacy of the reference signals. Numerical simulations validate the effectiveness of the proposed privacy-preserving DAC algorithm.

Privacy-Preserving Dynamic Average Consensus by Masking Reference Signals

TL;DR

Privacy in dynamic average consensus is challenged by state exchanges revealing private signals x_i(t). We propose a masking-based DAC that uses per-edge random values to form zero-sum masks m_i and masked references x_{m,i}(t) = x_i(t) + m_i, enabling the standard DAC update to run without exposing private signals. Theoretical results show external eavesdroppers cannot recover x_i(t) and honest-but-curious agents cannot uniquely infer a neighbor's reference when at least one neighbor is legitimate, while the convergence rate remains unchanged due to the preserved Laplacian structure; simulations on a ring network validate both privacy guarantees and performance on par with conventional DAC. This approach achieves privacy with low overhead and without sacrificing tracking accuracy, making it suitable for secure distributed control and resource allocation in networks.

Abstract

In multi-agent systems, dynamic average consensus (DAC) is a decentralized estimation strategy in which a set of agents tracks the average of time-varying reference signals. Because DAC requires exchanging state information with neighbors, attackers may gain access to these states and infer private information. In this paper, we develop a privacy-preserving method that protects each agent's reference signal from external eavesdroppers and honest-but-curious agents while achieving the same convergence accuracy and convergence rate as conventional DAC. Our approach masks the reference signals by having each agent draw a random real number for each neighbor, exchanges that number over an encrypted channel at the initialization, and computes a masking value to form a masked reference. Then the agents run the conventional DAC algorithm using the masked references. Convergence and privacy analyses show that the proposed algorithm matches the convergence properties of conventional DAC while preserving the privacy of the reference signals. Numerical simulations validate the effectiveness of the proposed privacy-preserving DAC algorithm.
Paper Structure (11 sections, 5 theorems, 29 equations, 5 figures)

This paper contains 11 sections, 5 theorems, 29 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Communication Network
  4. Dynamic Average Consensus Algorithm and Privacy Definition
  5. Main Results
  6. Privacy-Preserving Algorithm Design
  7. Privacy Analysis
  8. Privacy Analysis Against External Eavesdroppers
  9. Privacy Analysis Against Honest–but–Curious Agents
  10. Simulation Results
  11. Conclusion

Key Result

Lemma 1

kia2019tutorial If each input signal $x_i(t)$ in eq:1 is bounded, there exists a constant $\gamma>0$ such that, for any gain $\beta>0$, the estimate $\hat{x}_{{\rm a},i}(t)$ produced by eq:1 over a connected graph converges to a bounded neighborhood of $\tfrac{1}{N}\mathbf{1}_N\tt x(t)$ at an expone where $x(t) = [x_1(t)\; x_2(t)\,\dotsc\, x_N(t)]\tt$, and $\lambda_2$ is the smallest nonzero eige

Figures (5)

  • Figure 1: The communication topology
  • Figure 2: The estimator state $\hat{x}_{{\rm a},i}$ convergence.
  • Figure 3: Eavesdropper reconstruction of $x_i(t)$ ($\hat{x}_{\rm e,i}$) vs true reference signal $x_i(t)$ under the proposed algorithm.
  • Figure 4: An Honest-but-curious agent's (agent 2) reconstruction of $x_1(t)$ ($\hat{x}_{h,1}(t)$) vs true reference signal $x_i(t)$ under the proposed algorithm.
  • Figure 5: $\ell_2$-norm of the consensus error for the proposed privacy-preserving DAC vs the state-decomposition-based DAC.

Theorems & Definitions (10)

  • Remark 1
  • Lemma 1
  • Theorem 1
  • proof
  • Remark 2
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Corollary 1