Scalable Robust Safety Filter With Unknown Disturbance Set

Equipping any controller with formal safety guarantees can be achieved by using safety filters. These filters modify the desired control input in the least restrictive way to guarantee safety. However, it is an unresolved issue to construct scalable safety filters without assuming the availability of the disturbance set. In this article, we address this issue by proposing an efficient approach to implementing safety filters. In particular, we perform offline set membership identification to obtain a linear model that is conformant to a finite set of training data. Based on this conformant model, we compute a set-based safe backup controller with a corresponding safe set. Because a new measurement obtained online might invalidate the model conformance, we update the model, the safe backup controller, and the safe set online to restore formal safety guarantees. We use scalable reachability analysis and convex optimization algorithms to perform these updates as quickly as possible. We demonstrate the usefulness and scalability of our safety filter approach using four numerical examples from the literature.