Safe Learning-Based Feedback Linearization Tracking Control for Nonlinear System with Event-Triggered Model Update

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.