# Pareto Control Barrier Function for Inner Safe Set Maximization Under Input Constraints

arXiv: https://arxiv.org/abs/2410.04260 · HTML: https://mlsanity.com/paper/2410.04260/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 25 references that are in the map.
- First posted on arXiv 5 Oct 2024.

## Builds on (most cited first, 14 of 14)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Pareto Multi-Task Learning](https://mlsanity.com/paper/1912.12854/) (2019)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021)
- [How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems](https://mlsanity.com/paper/2310.15478/) (2023)
- [Safe Control Under Input Limits with Neural Control Barrier Functions](https://mlsanity.com/paper/2211.11056/) (2022)
- [Safe Control Synthesis via Input Constrained Control Barrier Functions](https://mlsanity.com/paper/2104.01704/) (2021)
- [Control Barrier Functions and Input-to-State Safety with Application to Automated Vehicles](https://mlsanity.com/paper/2206.03568/) (2022)
- [Learning Safe Control for Multi-Robot Systems: Methods, Verification, and Open Challenges](https://mlsanity.com/paper/2311.13714/) (2023)
- [RotorPy: A Python-based Multirotor Simulator with Aerodynamics for Education and Research](https://mlsanity.com/paper/2306.04485/) (2023)
- [High Relative Degree Control Barrier Functions Under Input Constraints](https://mlsanity.com/paper/2106.10345/) (2021)

## Abstract (arXiv)

This article introduces the Pareto Control Barrier Function (PCBF) algorithm to maximize the inner safe set of dynamical systems under input constraints. Traditional Control Barrier Functions (CBFs) ensure safety by maintaining system trajectories within a safe set but often fail to account for realistic input constraints. To address this problem, we leverage the Pareto multi-task learning framework to balance competing objectives of safety and safe set volume. The PCBF algorithm is applicable to high-dimensional systems and is computationally efficient. We validate its effectiveness through comparison with Hamilton-Jacobi reachability for an inverted pendulum and through simulations on a 12-dimensional quadrotor system. Results show that the PCBF consistently outperforms existing methods, yielding larger safe sets and ensuring safety under input constraints.