  In this paper, a distributed learning leader-follower consensus protocol
based on Gaussian process regression for a class of nonlinear multi-agent
systems with unknown dynamics is designed. We propose a distributed learning
approach to predict the residual dynamics for each agent. The stability of the
consensus protocol using the data-driven model of the dynamics is shown via
Lyapunov analysis. The followers ultimately synchronize to the leader with
guaranteed error bounds by applying the proposed control law with a high
probability. The effectiveness and the applicability of the developed protocol
are demonstrated by simulation examples.
