  Learning-based methods are powerful in handling complex scenarios. However,
it is still challenging to use learning-based methods under uncertain
environments while stability, safety, and real-time performance of the system
are desired to guarantee. In this paper, we propose a learning-based tracking
control scheme based on a feedback linearization controller in which uncertain
disturbances are approximated online using Gaussian Processes (GPs). Using the
predicted distribution of disturbances given by GPs, a Control Lyapunov
Function (CLF) and Control Barrier Function (CBF) based Quadratic Program is
applied, with which probabilistic stability and safety are guaranteed. In
addition, the trajectory is optimized first by Model Predictive Control (MPC)
based on the linearized dynamics systems to further reduce the tracking error.
We also design an event trigger for GPs updates to improve efficiency while
stability and safety of the system are still guaranteed. The effectiveness of
the proposed tracking control strategy is illustrated in numerical simulations.
