Safe Event-triggered Gaussian Process Learning for Barrier-Constrained Control

While control barrier functions (CBFs) are employed in addressing safety, control synthesis methods based on them generally rely on accurate system dynamics. This is a critical limitation, since the dynamics of complex systems are often not fully known. Supervised machine learning techniques hold great promise for alleviating this weakness by inferring models from data. We propose a novel \revision{approach for safe event-triggered learning of Gaussian process models in CBF-based continuous-time control for unknown control-affine systems. By applying a finite excitation at triggering times, our approach ensures a sufficient information gain to maintain the feasibility of the CBF-based safety condition with high probability. Our approach probabilistically guarantees safety based on a suitable GP prior and rules out} Zeno behavior in the triggering scheme. The effectiveness of the proposed approach and theory is demonstrated in simulations.