# Learning Robust and Correct Controllers from Signal Temporal Logic Specifications Using BarrierNet

arXiv: https://arxiv.org/abs/2304.06160 · HTML: https://mlsanity.com/paper/2304.06160/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 28 references that are in the map.
- First posted on arXiv 12 Apr 2023.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Q-Learning for Robust Satisfaction of Signal Temporal Logic Specifications](https://mlsanity.com/paper/1609.07409/) (2016)
- [Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods](https://mlsanity.com/paper/2008.00097/) (2020)
- [Control Barrier Functions for Systems with High Relative Degree](https://mlsanity.com/paper/1903.04706/) (2019)
- [On Robustness Metrics for Learning STL Tasks](https://mlsanity.com/paper/2003.06041/) (2020)
- [Tractable Reinforcement Learning of Signal Temporal Logic Objectives](https://mlsanity.com/paper/2001.09467/) (2020)
- [Robust Temporal Logic Model Predictive Control](https://mlsanity.com/paper/1511.00347/) (2015)
- [A Smooth Robustness Measure of Signal Temporal Logic for Symbolic Control](https://mlsanity.com/paper/2006.05239/) (2020)
- [Arithmetic-Geometric Mean Robustness for Control from Signal Temporal Logic Specifications](https://mlsanity.com/paper/1903.05186/) (2019)
- [Recurrent Neural Network Controllers for Signal Temporal Logic Specifications Subject to Safety Constraints](https://mlsanity.com/paper/2009.11468/) (2020)
- [Semi-Supervised Trajectory-Feedback Controller Synthesis for Signal Temporal Logic Specifications](https://mlsanity.com/paper/2202.01997/) (2022)
- [Model-Free Reinforcement Learning for Optimal Control of MarkovDecision Processes Under Signal Temporal Logic Specifications](https://mlsanity.com/paper/2109.13377/) (2021)
- [Robust Multi-Agent Coordination from CaTL+ Specifications](https://mlsanity.com/paper/2210.01732/) (2022)
- [High Order Control Lyapunov-Barrier Functions for Temporal Logic Specifications](https://mlsanity.com/paper/2102.06787/) (2021)
- [Safe Model-based Control from Signal Temporal Logic Specifications Using Recurrent Neural Networks](https://mlsanity.com/paper/2103.15938/) (2021)
- [Event-Triggered Safety-Critical Control for Systems with Unknown Dynamics](https://mlsanity.com/paper/2103.15874/) (2021)

## Built on by (most cited first, 6 of 6)

- [Four Principles for Physically Interpretable World Models](https://mlsanity.com/paper/2503.02143/) (2025)
- [TGPO: Temporal Grounded Policy Optimization for Signal Temporal Logic Tasks](https://mlsanity.com/paper/2510.00225/) (2025)
- [ABNet: Attention BarrierNet for Safe and Scalable Robot Learning](https://mlsanity.com/paper/2406.13025/) (2024)
- [Feasibility-aware Learning of Robust Temporal Logic Controllers using BarrierNet](https://mlsanity.com/paper/2512.06973/) (2025)
- [BarrierSteer: LLM Safety via Learning Barrier Steering](https://mlsanity.com/paper/2602.20102/) (2026)
- [Reward Machines for Signal Temporal Logic](https://mlsanity.com/paper/2608.13625/) (2026)

## Abstract (arXiv)

In this paper, we consider the problem of learning a neural network controller for a system required to satisfy a Signal Temporal Logic (STL) specification. We exploit STL quantitative semantics to define a notion of robust satisfaction. Guaranteeing the correctness of a neural network controller, i.e., ensuring the satisfaction of the specification by the controlled system, is a difficult problem that received a lot of attention recently. We provide a general procedure to construct a set of trainable High Order Control Barrier Functions (HOCBFs) enforcing the satisfaction of formulas in a fragment of STL. We use the BarrierNet, implemented by a differentiable Quadratic Program (dQP) with HOCBF constraints, as the last layer of the neural network controller, to guarantee the satisfaction of the STL formulas. We train the HOCBFs together with other neural network parameters to further improve the robustness of the controller. Simulation results demonstrate that our approach ensures satisfaction and outperforms existing algorithms.