  Consensus control in multi-agent systems has received significant attention
and practical implementation across various domains. However, managing
consensus control under unknown dynamics remains a significant challenge for
control design due to system uncertainties and environmental disturbances. This
paper presents a novel learning-based distributed control law, augmented by an
auxiliary dynamics. Gaussian processes are harnessed to compensate for the
unknown components of the multi-agent system. For continuous enhancement in
predictive performance of Gaussian process model, a data-efficient online
learning strategy with a decentralized event-triggered mechanism is proposed.
Furthermore, the control performance of the proposed approach is ensured via
the Lyapunov theory, based on a probabilistic guarantee for prediction error
bounds. To demonstrate the efficacy of the proposed learning-based controller,
a comparative analysis is conducted, contrasting it with both conventional
distributed control laws and offline learning methodologies.
