Safety-Critical Randomized Event-Triggered Learning of Gaussian Process With Applications to Data-Driven Predictive Control

Safety and data efficiency are important concerns in data-driven control, especially for nonlinear systems with unknown dynamics and subject to disturbances. In this work, we consider a class of control-affine nonlinear systems with partially unknown dynamics and aim to introduce an event-triggered learning-based control approach with guaranteed safety and improved data utilization efficiency. Specifically, a randomized learning approach is employed to evaluate the safety of state trajectories by defining and estimating its confidence interval, with data from a multisample of randomly generated state trajectories. Using the proposed randomized learning algorithm, a nominal trajectory with a high probability safety guarantee is designed, thus ensuring the disturbed system states to remain within a pre-specified range around the nominal trajectory with a sufficiently high probability. Through removing irrelevant data, a local prediction model around the nominal trajectory is learned with satisfactory precision, and is updated online using an event-triggered learning strategy. Based on the learned model, an efficient data-driven predictive controller is designed to force the system states to evolve within the vicinity of the designed safety nominal trajectory. The effectiveness of the proposed event-triggered learning and data-driven control approaches is validated through comprehensive simulation studies.