# Sufficient Conditions for Feasibility of Optimal Control Problems Using Control Barrier Functions

arXiv: https://arxiv.org/abs/2011.08248 · HTML: https://mlsanity.com/paper/2011.08248/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2020.

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

- [Differentiable Control Barrier Functions for Vision-based End-to-End Autonomous Driving](https://mlsanity.com/paper/2203.02401/) (2022)
- [Enhancing System-Level Safety in Mixed-Autonomy Platoon via Safe Reinforcement Learning](https://mlsanity.com/paper/2401.11148/) (2024)
- [On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach](https://mlsanity.com/paper/2305.03608/) (2023)
- [Safe Neural Control for Non-Affine Control Systems with Differentiable Control Barrier Functions](https://mlsanity.com/paper/2309.04492/) (2023)
- [Learning Feasibility Constraints for Control Barrier Functions](https://mlsanity.com/paper/2303.09403/) (2023)
- [Risk-aware Safe Control for Decentralized Multi-agent Systems via Dynamic Responsibility Allocation](https://mlsanity.com/paper/2305.13467/) (2023)
- [Safe PDE Boundary Control with Neural Operators](https://mlsanity.com/paper/2411.15643/) (2024)

## Abstract (arXiv)

It has been shown that satisfying state and control constraints while optimizing quadratic costs subject to desired (sets of) state convergence for affine control systems can be reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). One of the main challenges in this approach is ensuring the feasibility of these QPs, especially under tight control bounds and safety constraints of high relative degree. In this paper, we provide sufficient conditions for guranteed feasibility. The sufficient conditions are captured by a single constraint that is enforced by a CBF, which is added to the QPs such that their feasibility is always guaranteed. The additional constraint is designed to be always compatible with the existing constraints, therefore, it cannot make a feasible set of constraints infeasible - it can only increase the overall feasibility. We illustrate the effectiveness of the proposed approach on an adaptive cruise control problem.