  This paper proposes a novel control design for voltage tracking of an
islanded AC microgrid in the presence of {nonlinear} loads and parametric
uncertainties at the primary level of control. The proposed method is based on
the Tube-Based Robust Model Predictive Control (RMPC), an online
optimization-based method which can handle the constraints and uncertainties as
well. The challenge with this method is the conservativeness imposed by
designing the tube based on the worst-case scenario of the uncertainties. This
weakness is amended in this paper by employing a combination of a
learning-based Gaussian Process (GP) regression and RMPC. The advantage of
using GP is that both the mean and variance of the loads are predicted at each
iteration based on the real data, and the resulted values of mean and the bound
of confidence are utilized to design the tube in RMPC. The theoretical results
are also provided to prove the recursive feasibility and stability of the
proposed learning based RMPC. Finally, the simulation results are carried out
on both single and multiple DG (Distributed Generation) units.
