Differentially private consensus algorithm for continuous-time heterogeneous multi-agent systems

This paper investigates the differential private algorithm for the average output consensus control of continuous-time heterogeneous systems. A distributed hybrid controller is designed where agents exchange information at discrete time instants. The proposed controller protects the individual privacy by imposing random noises upon the interactive information. Based on the stochastic approximation method, we employ a series of time-varying control gains to relax the existing mechanisms which require the privacy noises to be exponentially decaying with time. Using non-decaying privacy noises, the delivered information can keep random with an invariant variance, and the real information cannot be directly exposed to the eavesdropper along with time. We further develop a method to design the control gain such that the heterogeneous systems can achieve asymptotically unbiased output average consensus with the desired accuracy and meet the predefined differential privacy index. Finally, a numerical example is provided to demonstrate the effectiveness of the theoretical results.