# Soft-Minimum Barrier Functions for Safety-Critical Control Subject to Actuation Constraints

arXiv: https://arxiv.org/abs/2304.00693 · HTML: https://mlsanity.com/paper/2304.00693/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2023.

## Built on by (most cited first, 3 of 3)

- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (2024)
- [Domain Adaptive Safety Filters via Deep Operator Learning](https://mlsanity.com/paper/2410.14528/) (2024)
- [Text-Conditioned Background Generation for Editable Multi-Layer Documents](https://mlsanity.com/paper/2512.17151/) (2025)

## Abstract (arXiv)

This paper presents a new control approach for guaranteed safety (remaining in a safe set) subject to actuator constraints (the control is in a convex polytope). The control signals are computed using real-time optimization, including linear and quadratic programs subject to affine constraints, which are shown to be feasible. The control method relies on a new soft-minimum barrier function that is constructed using a finite-time-horizon prediction of the system trajectories under a known backup control. The main result shows that: (i) the control is continuous and satisfies the actuator constraints, and (ii) a subset of the safe set is forward invariant under the control. We also demonstrate this control on numerical simulations of an inverted pendulum and a double-integrator ground robot.