Tunable Real-Time Safety Filters via Set-Based Control Barrier Functions

arXiv:2507.07805v3 Announce Type: replace Abstract: Safety filters for industrial constrained systems are required to combine certified constraint satisfaction, predictable online computation, and a transparent tuning interface. Existing set-based filters are based on a well-established control invariant set design that scales favorably with state and input constraints, but typically intervene only at the set boundary. Control barrier function (CBF)-based filters, by contrast, provide tunable intervention but require a scalar barrier construction. This paper proposes a set-based CBF safety filter that turns a convex control invariant set directly into a tunable barrier via its Minkowski functional. The resulting filter is formulated as a single-level quadratic program (QP) in which one class-$\mathcal{K}^e$ parameter sets the intervention aggressiveness. Explicit convex formulations are derived for polytopic, zonotopic, and MPC-based invariant sets. Under standard bounded-disturbance assumptions, the resulting safety filter guarantees constraint satisfaction and asymptotic recovery into the invariant set. For tight real-time budgets, a learning-based approximation enables online acceleration, while the formal safety guarantees remain tied to the exact formulation. The method is validated in numerical studies and on a permanent-magnet synchronous motor drive, where an explicit QP implementation evaluates within a 150 microseconds sampling window and has a worst-case execution time of 28.04 microseconds.