Differentially private containment control for multi-agent systems

This paper is concerned with the differential privacy-based containment control problem for a class of discrete-time multi-agent systems (MASs) with time-varying topology. The classical containment control implementation relies on the explicit information exchange between agents, which will lead to the possible leakage of agents' private information, especially the initial states. In this paper, to prevent such data disclosure to neighbours inside the MASs and the outside eavesdroppers, uncorrelated noise is injected into the data during information transmission, which will bring about a more complicated scenario to the containment control. Under a milder assumption on the connectivity of the MAS – ‘average graph topology’, by resorting to the Lyapunov stability theory and algebraic graph theory, and utilising stochastic analysis techniques, sufficient conditions are derived to ensure that the discrete-time MAS subjecting to the privacy protection mechanism can achieve bounded containment control. Then, convergence accuracy is studied from the viewpoint of probability. Specially, Markov inequality is first utilised to estimate the lower bound of the probability that followers' states converge to the neighbourhood of the convex hull formed by leaders' states. Besides, differential privacy analysis is carried out to verify the validity of the proposed privacy protection mechanism in protecting the followers' initial states. Finally, two numerical examples are simulated to verify the theoretical results.