Stability Mechanisms for Predictive Safety Filters

Predictive safety filters enable the integration of potentially unsafe learning-based control approaches and humans into safety-critical systems. In addition to simple constraint satisfaction, many control problems involve additional stability requirements that may vary depending on the specific use case or environmental context. In this work, we address this problem by augmenting predictive safety filters with stability guarantees, ranging from bounded convergence to uniform asymptotic stability. The proposed framework extends wellknown stability results from model predictive control (MPC) theory while supporting commonly used design techniques. As a result, straightforward extensions to dynamic trajectory tracking problems can be easily adapted, as outlined in this article. The practicality of the framework is demonstrated using an automotive advanced driver assistance scenario, involving a reference trajectory stabilization problem.