# Robust Control Barrier Functions with Sector-Bounded Uncertainties

arXiv: https://arxiv.org/abs/2109.02537 · HTML: https://mlsanity.com/paper/2109.02537/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2021.

## Built on by (most cited first, 9 of 9)

- [Synthesis of Stabilizing Recurrent Equilibrium Network Controllers](https://mlsanity.com/paper/2204.00122/) (2022)
- [Learning Control Barrier Functions and their application in Reinforcement Learning: A Survey](https://mlsanity.com/paper/2404.16879/) (2024)
- [Synthesis and Deployment of Maximal Robust Control Barrier Functions through Adversarial Reinforcement Learning](https://mlsanity.com/paper/2604.13192/) (2026)
- [ConBaT: Control Barrier Transformer for Safe Policy Learning](https://mlsanity.com/paper/2303.04212/) (2023)
- [Learning Predictive Safety Filter via Decomposition of Robust Invariant Set](https://mlsanity.com/paper/2311.06769/) (2023)
- [DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safety](https://mlsanity.com/paper/2407.00616/) (2024)
- [SAD-Flower: Flow Matching for Safe, Admissible, and Dynamically Consistent Planning](https://mlsanity.com/paper/2511.05355/) (2025)
- [Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions](https://mlsanity.com/paper/2208.10733/) (2022)
- [Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models](https://mlsanity.com/paper/2402.18946/) (2024)

## Abstract (arXiv)

This paper focuses on safety critical control with sector-bounded uncertainties at the plant input. The uncertainties can represent nonlinear and/or time-varying components. We propose a new robust control barrier function (RCBF) approach to enforce safety requirements in the presence of these uncertainties. The primary objective is to minimally alter the given baseline control command to guarantee safety in the presence of modeled uncertainty. The resulting min-norm optimization problem can be recast as a Second-Order Cone Program (SOCP) to enable online implementation. Properties of this controller are studied and a numerical example is provided to illustrate the effectiveness of this approach.