Predictive Control Barrier Functions: Enhanced Safety Mechanisms for Learning-Based Control

While learning-based control techniques often outperform classical controller designs, safety requirements limit the acceptance of such methods in many applications. Recent developments address this issue through so-called predictive filters, which assess if a proposed input can lead to constraint violations and modifies it necessary ensure for all future time steps. The theoretical guarantees filters rely on model assumptions minor deviations failure filter putting system at risk. This paper introduces an auxiliary soft-constrained problem that is always feasible each step asymptotically stabilizes set original filter, thereby providing recovery mechanism safety-critical situations. achieved by simple tightening combination with terminal barrier function. By extending discrete-time function theory, we establish provides ‘predictive’ resulting algorithm demonstrated using numerical examples.