Safe Barrier-Constrained Control of Uncertain Systems via Event-triggered Learning

Abstract: While control barrier functions 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 control barrier function-based framework for safe control through event-triggered learning, which switches between prioritizing control performance and improving model accuracy based on the uncertainty of the learned model. By updating a Gaussian process model with training points gathered online, the approach guarantees the feasibility of control barrier function conditions with high probability, such that safety can be ensured in a data-efficient manner. Furthermore, we establish the absence of Zeno behavior in the triggering scheme, and extend the algorithm to sampled-data realizations by accounting for inter-sampling effects. The effectiveness of the proposed approach and theory is demonstrated in simulations.