# High Order Control Lyapunov-Barrier Functions for Temporal Logic Specifications

arXiv: https://arxiv.org/abs/2102.06787 · HTML: https://mlsanity.com/paper/2102.06787/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2021.

## Built on by (most cited first, 3 of 3)

- [Learning Robust and Correct Controllers from Signal Temporal Logic Specifications Using BarrierNet](https://mlsanity.com/paper/2304.06160/) (2023)
- [Safe PDE Boundary Control with Neural Operators](https://mlsanity.com/paper/2411.15643/) (2024)
- [Feasibility-aware Learning of Robust Temporal Logic Controllers using BarrierNet](https://mlsanity.com/paper/2512.06973/) (2025)

## Abstract (arXiv)

Recent work has shown that stabilizing an affine control system to a desired state while optimizing a quadratic cost subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). In our own recent work, we defined High Order CBFs (HOCBFs) for systems and constraints with arbitrary relative degrees. In this paper, in order to accommodate initial states that do not satisfy the state constraints and constraints with arbitrary relative degree, we generalize HOCBFs to High Order Control Lyapunov-Barrier Functions (HOCLBFs). We also show that the proposed HOCLBFs can be used to guarantee the Boolean satisfaction of Signal Temporal Logic (STL) formulae over the state of the system. We illustrate our approach on a safety-critical optimal control problem (OCP) for a unicycle.