Differentially Private Average Consensus With Logarithmic Dynamic Encoding-Decoding Scheme.

Area of Science:

• Control Theory
• Information Security
• Distributed Systems

Background:

• Multiagent systems require robust consensus algorithms for coordinated behavior.
• Quantized communication introduces errors that degrade consensus accuracy.
• Ensuring differential privacy is crucial for sensitive data in distributed systems.

Purpose of the Study:

• To develop a differentially private average consensus (DPAC) algorithm for multiagent systems with quantized communication.
• To establish a unified framework for analyzing convergence, accuracy, and privacy of the DPAC algorithm.
• To mitigate the impact of quantization errors on consensus accuracy using a novel communication scheme.

Main Methods:

• Development of a logarithmic dynamic encoding-decoding (LDED) scheme to eliminate quantization errors.
• Application of matrix eigenvalue analysis and Jury stability criterion for convergence analysis.
• Utilization of Chebyshev inequality and epsilon-differential privacy index for accuracy and privacy evaluation.

Main Results:

• A sufficient condition for almost sure convergence of the DPAC algorithm was derived, considering quantization accuracy, coupling strength, and communication topology.
• The LDED scheme effectively eliminates quantization errors, preserving consensus accuracy.
• The framework provides a thorough investigation of convergence accuracy and privacy levels.

Conclusions:

• The proposed DPAC algorithm with LDED scheme ensures both convergence and differential privacy in quantized communication environments.
• The unified framework offers a comprehensive approach to analyzing such systems.
• Simulation results validate the algorithm's correctness and effectiveness.