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This paper considers the problem of privacy preservation against passiveinternal and external malicious agents in the continuous-time Laplacian averageconsensus algorithm over strongly connected and weight-balanced digraphs. Forthis problem, we evaluate the effectiveness of use of additive perturbationsignals as a privacy preservation measure against malicious agents that knowthe graph topology. Our results include (a) identifying the necessary andsufficient conditions on admissible additive perturbation signals that do notperturb the convergence point of the algorithm from the average of initialvalues of the agents; (b) obtaining the necessary and sufficient condition onthe knowledge set of a malicious agent that enables it to identify the initialvalue of another agent; (c) designing observers that internal and externalmalicious agents can use to identify the initial conditions of another agentwhen their knowledge set on that agent enables them to do so. We demonstrateour results through a numerical example.

Privacy preservation in continuous-time average consensus algorithm via deterministic additive obfuscation signals