# Compositions of Multiple Control Barrier Functions Under Input Constraints

arXiv: https://arxiv.org/abs/2210.01354 · HTML: https://mlsanity.com/paper/2210.01354/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Oct 2022.

## Built on by (most cited first, 5 of 5)

- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (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)
- [Domain Adaptive Safety Filters via Deep Operator Learning](https://mlsanity.com/paper/2410.14528/) (2024)
- [Neural Control Barrier Functions from Physics Informed Neural Networks](https://mlsanity.com/paper/2504.11045/) (2025)
- [Feasibility-aware Learning of Robust Temporal Logic Controllers using BarrierNet](https://mlsanity.com/paper/2512.06973/) (2025)

## Abstract (arXiv)

This paper presents a methodology for ensuring that the composition of multiple Control Barrier Functions (CBFs) always leads to feasible conditions on the control input, even in the presence of input constraints. In the case of a system subject to a single constraint function, there exist many methods to generate a CBF that ensures constraint satisfaction. However, when there are multiple constraint functions, the problem of finding and tuning one or more CBFs becomes more challenging, especially in the presence of input constraints. This paper addresses this challenge by providing tools to 1) decouple the design of multiple CBFs, so that a CBF can be designed for each constraint function independently of other constraints, and 2) ensure that the set composed from all the CBFs together is a viability domain. Thus, a quadratic program subject to all the CBFs simultaneously is always feasible. The utility of this methodology is then demonstrated in simulation for a nonlinear orientation control system.