Privacy preservation in a continuous-time static average consensus algorithm over directed graphs

In this paper, we study the problem of privacy preservation of the continuous-time Laplacian static average consensus algorithm using additive perturbation signals. We consider this problem over a strongly connected and weight-balanced digraph. Starting from a local reference value, in static average consensus algorithm each agent constantly communicates with its neighboring agents to update its local state to compute the average of the reference values across the network. Since every agent transmits its local reference value to its in-neighbors, the reference value of the agents are trivially disclosed. In this paper, we investigate the possibility of preserving the privacy of the reference value of the agents by adding admissible perturbation signals to the local dynamics and the transmitted out signals of the agents. Admissible additive perturbation signals are those signals that do not perturb the final convergence point of the algorithm from the average of the reference values of the agents. Our results show that if an adversarial agent has access to the output of another agent and all the input signals transmitted to that agent, the adversary can discover the private reference value of that agent, regardless of the perturbation signals. Otherwise, the privacy of the agent can be preserved. We demonstrate our results through a numerical example.