# Advances in the Theory of Control Barrier Functions: Addressing Practical Challenges in Safe Control Synthesis for Autonomous and Robotic Systems

arXiv: https://arxiv.org/abs/2312.16719 · HTML: https://mlsanity.com/paper/2312.16719/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Dec 2023.

## Built on by (most cited first, 6 of 6)

- [Neuro-Symbolic Safety Guidance for Vision-Language-Action Models via Constrained Flow Matching](https://mlsanity.com/paper/2607.01378/) (2026)
- [ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworks](https://mlsanity.com/paper/2509.16614/) (2025)
- [Safe Heterogeneous Multi-Agent RL with Communication Regularization for Coordinated Target Acquisition](https://mlsanity.com/paper/2601.08327/) (2026)
- [Neural Network-assisted Interval Reachability for Systems with Control Barrier Function-Based Safe Controllers](https://mlsanity.com/paper/2504.08249/) (2025)
- [Tail-Safe Hedging: Explainable Risk-Sensitive Reinforcement Learning with a White-Box CBF--QP Safety Layer in Arbitrage-Free Markets](https://mlsanity.com/paper/2510.04555/) (2025)
- [Set-Based Training of Neural Barrier Certificates for Safety Verification of Dynamical Systems](https://mlsanity.com/paper/2605.02526/) (2026)

## Abstract (arXiv)

This tutorial paper presents recent work of the authors that extends the theory of Control Barrier Functions (CBFs) to address practical challenges in the synthesis of safe controllers for autonomous systems and robots. We present novel CBFs and methods that handle safety constraints (i) with time and input constraints under disturbances, (ii) with high-relative degree under disturbances and input constraints, and (iii) that are affected by adversarial inputs and sampled-data effects. We then present novel CBFs and adaptation methods that prevent loss of validity of the CBF, as well as methods to tune the parameters of the CBF online to reduce conservatism in the system response. We also address the pointwise-only optimal character of CBF-induced control inputs by introducing a CBF formulation that accounts for future trajectories, as well as implementation challenges such as how to preserve safety when using output feedback control and zero-order-hold control. Finally we consider how to synthesize non-smooth CBFs when discontinuous inputs and multiple constraints are present.