Privacy Preserving Second-Order Consensus by Adding Edge-Based Perturbations

Many works on privacy-preserving consensus of multi-agents are limited to first-order dynamics, and developing privacy-preserving consensus algorithms based on second-order dynamical network systems has a stronger need for engineering practicality and presents a greater challenge. In this paper, we propose a privacy-preserving second-order consensus algorithm based on strongly connected directed graphs. The algorithm avoids direct interaction of real states among individuals by adding well-designed perturbation signals based on commu-nication edges. Theoretical results indicate that the proposed algorithm is able to achieve accurate second-order dynamic consensus. Moreover, through rigid theoretical analysis, we give necessary and sufficient conditions for an agent to maintain its position and velocity privacy in the face of an internal honest-but-curious agent. Simulation examples verify the effectiveness of the proposed algorithm.