# Safe Control Synthesis via Input Constrained Control Barrier Functions

arXiv: https://arxiv.org/abs/2104.01704 · HTML: https://mlsanity.com/paper/2104.01704/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2021.

## Built on by (most cited first, 13 of 13)

- [Safe Control Under Input Limits with Neural Control Barrier Functions](https://mlsanity.com/paper/2211.11056/) (2022)
- [Exact Verification of ReLU Neural Control Barrier Functions](https://mlsanity.com/paper/2310.09360/) (2023)
- [Real-Time Safe Control of Neural Network Dynamic Models with Sound Approximation](https://mlsanity.com/paper/2404.13456/) (2024)
- [Demonstrating Reinforcement Learning and Run Time Assurance for Spacecraft Inspection Using Unmanned Aerial Vehicles](https://mlsanity.com/paper/2405.06770/) (2024)
- [Multi-Constraint Safe Reinforcement Learning via Closed-form Solution for Log-Sum-Exp Approximation of Control Barrier Functions](https://mlsanity.com/paper/2505.00671/) (2025)
- [Meta-Reinforcement Learning for Robust and Non-greedy Control Barrier Functions in Spacecraft Proximity Operations](https://mlsanity.com/paper/2602.07335/) (2026)
- [Safe PDE Boundary Control with Neural Operators](https://mlsanity.com/paper/2411.15643/) (2024)
- [Learning Safety-Guaranteed, Non-Greedy Control Barrier Functions Using Reinforcement Learning](https://mlsanity.com/paper/2602.00366/) (2026)
- [Pareto Control Barrier Function for Inner Safe Set Maximization Under Input Constraints](https://mlsanity.com/paper/2410.04260/) (2024)
- [Neural Network-assisted Interval Reachability for Systems with Control Barrier Function-Based Safe Controllers](https://mlsanity.com/paper/2504.08249/) (2025)
- [Real-Time Model Checking for Closed-Loop Robot Reactive Planning](https://mlsanity.com/paper/2508.19186/) (2025)
- [Constrained Whole-Body Tracking for Humanoid Robots](https://mlsanity.com/paper/2606.00374/) (2026)
- [Memory-Efficient Meta-Reinforcement Learning for Adaptive Safety-Critical Control in Adversarial Spacecraft Proximity Operations](https://mlsanity.com/paper/2606.17414/) (2026)

## Abstract (arXiv)

This paper introduces the notion of an Input Constrained Control Barrier Function (ICCBF), as a method to synthesize safety-critical controllers for non-linear control affine systems with input constraints. The method identifies a subset of the safe set of states, and constructs a controller to render the subset forward invariant. The feedback controller is represented as the solution to a quadratic program, which can be solved efficiently for real-time implementation. Furthermore, we show that ICCBFs are a generalization of Higher Order Control Barrier Functions, and thus are applicable to systems of non-uniform relative degree. Simulation results are presented for the adaptive cruise control problem, and a spacecraft rendezvous problem.