  Data-driven Model Predictive Control (MPC), where the system model is learned
from data with machine learning, has recently gained increasing interests in
the control community. Gaussian Processes (GP), as a type of statistical
models, are particularly attractive due to their modeling flexibility and their
ability to provide probabilistic estimates of prediction uncertainty. GP-based
MPC has been developed and applied, however the optimization problem is
typically non-convex and highly demanding, and scales poorly with model size.
This causes unsatisfactory solving performance, even with state-of-the-art
solvers, and makes the approach less suitable for real-time control. We develop
a method based on a new concept, called linearized Gaussian Process, and
Sequential Convex Programming, that can significantly improve the solving
performance of GP-based MPC. Our method is not only faster but also much more
scalable and predictable than other commonly used methods, as it is much less
influenced by the model size. The efficiency and advantages of the algorithm
are demonstrated clearly in a numerical example.
