Enforcing safety at runtime for systems with disturbances

M. Abate, S. Coogan
IEEE Conference on Decision and Control, 2020


An assured controller is one that enforces safety online by filtering a desired control input at runtime, and control barrier functions (CBFs) provide an assured controller that renders a safe subset of the statespace forward invariant. In this work, we present a problem formulation for CBF- based runtime assurance for systems with disturbances, and controllers that solve this problem must, in some way, incorporate the online computation of reachable sets. In general, computing reachable sets in the presence of disturbances is computationally costly and cannot be directly incorporated in a CBF framework. To that end, we present a particular solution to the problem, whereby reachable sets are approximated via the mixed-monotonicity property. Efficient algorithms exist for over-approximating reachable sets for mixed-monotone systems with hyperrectangles, and we show that such approximations are suitable for incorporating into a CBF-based runtime assurance framework.