Privacy preserving average consensus

Average consensus is a widely used algorithm for distributed computing and control, where all the agents in the network constantly communicate and update their states in order to achieve an agreement. This approach could result in an undesirable disclosure of information on the initial state of agent i to the other agents. In this paper, we propose a privacy preserving average consensus algorithm to guarantee the privacy of the initial state and the convergence of the algorithm to the exact average of the initial values, by adding and subtracting random noises to the consensus process. We characterize the mean square convergence rate of our consensus algorithm and derive upper and lower bounds for the covariance matrix of the maximum likelihood estimate on the initial state. A numerical example is provided to illustrate the effectiveness of the proposed design.