# Data-Driven Time-Varying Control Barrier Functions for Adaptive Safe-Set Learning with Online Decremental Support Vector Machines

arXiv: https://arxiv.org/abs/2608.19366 · HTML: https://mlsanity.com/paper/2608.19366/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 19 Aug 2026.

## Builds on (most cited first, 8 of 8)

- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems](https://mlsanity.com/paper/2310.15478/) (2023)
- [Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach](https://mlsanity.com/paper/2003.04950/) (2020)
- [Robust Control Barrier Functions using Uncertainty Estimation with Application to Mobile Robots](https://mlsanity.com/paper/2401.01881/) (2024)
- [Collision Avoidance and Geofencing for Fixed-wing Aircraft with Control Barrier Functions](https://mlsanity.com/paper/2403.02508/) (2024)
- [Time-Varying Soft-Maximum Barrier Functions for Safety in Unmapped and Dynamic Environments](https://mlsanity.com/paper/2409.01458/) (2024)

## Abstract (arXiv)

Mission-critical intelligent systems often operate under time-varying limitations that reduce control authority and change the admissible safe operating envelope. In such settings, a safety certificate learned under nominal conditions may become invalid as system capability changes. To address this challenge, this paper proposes a degradation-aware, data-driven safety-filtering framework that learns a safe set from data, updates it online, and enforces the resulting learned barrier through a time-varying control barrier function (CBF). A nominal safe envelope is first learned from operational data using a radial basis function (RBF)-kernel support vector machine (SVM), whose decision function serves as the initial CBF candidate. To capture capability-induced safe-set contraction, a continuous-time decremental SVM update law is developed so that selected support-vector coefficients are reduced according to a degradation signal. A homotopy-smoothed SVM-CBF is then introduced to avoid discontinuous changes in the learned barrier during active-set transitions. The resulting time-varying learned barrier is enforced using a quadratic-program-based safety filter under degraded input constraints. Forward invariance of the learned time-varying safe set and recursive feasibility of the safety filter are established. Simulation results on a vertical takeoff and landing (VTOL) model show that the proposed method maintains safety under reduced control authority and avoids abrupt barrier-switching effects during safe-set contraction.