# Integral Control Barrier Functions for Dynamically Defined Control Laws

arXiv: https://arxiv.org/abs/2006.16936 · HTML: https://mlsanity.com/paper/2006.16936/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2020.

## Built on by (most cited first, 7 of 7)

- [On the Forward Invariance of Neural ODEs](https://mlsanity.com/paper/2210.04763/) (2022)
- [Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach](https://mlsanity.com/paper/2208.02319/) (2022)
- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (2024)
- [Safe Neural Control for Non-Affine Control Systems with Differentiable Control Barrier Functions](https://mlsanity.com/paper/2309.04492/) (2023)
- [Learning Exactly Linearizable Deep Dynamics Models](https://mlsanity.com/paper/2311.18261/) (2023)
- [Domain Adaptive Safety Filters via Deep Operator Learning](https://mlsanity.com/paper/2410.14528/) (2024)
- [TRUST-UP: Trustworthy Reinforcement learning Using Safe Techniques for UAV Pursuit](https://mlsanity.com/paper/2411.17552/) (2024)

## Abstract (arXiv)

This paper introduces integral control barrier functions (I-CBFs) as a means to enable the safety-critical integral control of nonlinear systems. Importantly, I-CBFs allow for the holistic encoding of both state constraints and input bounds in a single framework. We demonstrate this by applying them to a dynamically defined tracking controller, thereby enforcing safety in state and input through a minimally invasive I-CBF controller framed as a quadratic program.