Robust Constrained Consensus with Guaranteed Differential Privacy and Accurate Convergence

Not only is constrained consensus widely used in cooperative control and sensor networks, it is also a fundamental building block in numerous distributed computation algorithms such as multi-agent optimization and distributed Nash equilibrium seeking. We propose a new robust constrained consensus algorithm that is robust to persistent and independent noises added for the purpose of differential-privacy protection. In fact, the algorithm can ensure both accurate consensus and rigorous ϵ-differential privacy (even when the number of iterations tends to infinity), which, to our knowledge, has not been achieved before in constrained consensus algorithms. Since channel noise in communications can be viewed as a special case of differential-privacy noises, the algorithm can also be used to counteract communication imperfections. Numerical simulation results confirm the effectiveness of the proposed approach.