  Model Predictive Control (MPC) of an unknown system that is modelled by
Gaussian Process (GP) techniques is studied in this paper. Using GP, the
variances computed during the modelling and inference processes allow us to
take model uncertainty into account. The main issue in using MPC to control
systems modelled by GP is the propagation of such uncertainties within the
control horizon. In this paper, two approaches to solve this problem, called
GPMPC1 and GPMPC2, are proposed. With GPMPC1, the original Stochastic Model
Predictive Control (SMPC) problem is relaxed to a deterministic nonlinear MPC
based on a basic linearized GP local model. The resulting optimization problem,
though non-convex, can be solved by the Sequential Quadratic Programming (SQP).
By incorporating the model variance into the state vector, an extended local
model is derived. This model allows us to relax the non-convex MPC problem to a
convex one which can be solved by an active-set method efficiently. The
performance of both approaches is demonstrated by applying them to two
trajectory tracking problems. Results show that both GPMPC1 and GPMPC2 produce
effective controls but GPMPC2 is much more efficient computationally.
