Enforcing Safety at Runtime for Systems with Disturbances

TL;DR

This paper develops a runtime safety assurance framework for control systems with disturbances using control barrier functions and efficient reachable set approximations based on mixed-monotonicity.

Contribution

It introduces a novel formulation for CBF-based safety assurance in disturbed systems and proposes an efficient approximation method for reachable sets using mixed-monotonicity.

Findings

Reachable set approximation via mixed-monotonicity is effective for disturbed systems.

The proposed method enables real-time safety assurance with computational efficiency.

The framework extends existing CBF approaches to systems with unknown disturbances.

Abstract

Safety for control systems is often posed as an invariance constraint; the system is said to be safe if state trajectories avoid some unsafe region of the statespace for all time. 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 state-space forward invariant. Recent extensions propose CBF-based assured controllers that allow the system to leave a known safe set so long as a given backup control strategy eventually returns to the safe set, however, these methods have yet to be extended to consider systems subjected to unknown disturbance inputs. In this work, we present a problem formulation for CBF-based runtime assurance for systems with disturbances, and controllers which 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 overapproximating 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.