Differentially Private Average Consensus With Logarithmic Dynamic Encoding–Decoding Scheme

This article is concerned with the differentially private average consensus (DPAC) problem for a class of multiagent systems with quantized communication. By constructing a pair of auxiliary dynamic equations, a logarithmic dynamic encoding–decoding (LDED) scheme is developed and then utilized during the process of data transmission, thereby eliminating the effect of quantization errors on the consensus accuracy. The primary purpose of this article is to establish a unified framework that integrates the convergence analysis, the accuracy evaluation, and the privacy level for the developed DPAC algorithm under the LDED communication scheme. By means of the matrix eigenvalue analysis method, the Jury stability criterion, and the probability theory, a sufficient condition (with respect to the quantization accuracy, the coupling strength, and the communication topology) is first derived to ensure the almost sure convergence of the proposed DPAC algorithm, and the convergence accuracy and privacy level are thoroughly investigated by resorting to the Chebyshev inequality and $\epsilon $ -differential privacy index. Finally, simulation results are provided to illustrate the correctness and validity of the developed algorithm.