# Safe Model-based Control from Signal Temporal Logic Specifications Using Recurrent Neural Networks

arXiv: https://arxiv.org/abs/2103.15938 · HTML: https://mlsanity.com/paper/2103.15938/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 29 Mar 2021.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [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)
- [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)
- [Modular Deep Reinforcement Learning for Continuous Motion Planning with Temporal Logic](https://mlsanity.com/paper/2102.12855/) (2021)
- [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)
- [A Policy Search Method For Temporal Logic Specified Reinforcement Learning Tasks](https://mlsanity.com/paper/1709.09611/) (2017)
- [Recurrent Neural Network Controllers for Signal Temporal Logic Specifications Subject to Safety Constraints](https://mlsanity.com/paper/2009.11468/) (2020)
- [Control from Signal Temporal Logic Specifications with Smooth Cumulative Quantitative Semantics](https://mlsanity.com/paper/1904.11611/) (2019)
- [On-Line Monitoring for Temporal Logic Robustness](https://mlsanity.com/paper/1408.0045/) (2014)
- [Continuous Motion Planning with Temporal Logic Specifications using Deep Neural Networks](https://mlsanity.com/paper/2004.02610/) (2020)
- [Prescribed Performance Control Guided Policy Improvement for Satisfying Signal Temporal Logic Tasks](https://mlsanity.com/paper/1903.04340/) (2019)

## 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)
- [Interpretable Imitation Learning via Generative Adversarial STL Inference and Control](https://mlsanity.com/paper/2402.10310/) (2024)
- [Feasibility-aware Learning of Robust Temporal Logic Controllers using BarrierNet](https://mlsanity.com/paper/2512.06973/) (2025)

## Abstract (arXiv)

We propose a policy search approach to learn controllers from specifications given as Signal Temporal Logic (STL) formulae. The system model, which is unknown but assumed to be an affine control system, is learned together with the control policy. The model is implemented as two feedforward neural networks (FNNs) - one for the drift, and one for the control directions. To capture the history dependency of STL specifications, we use a recurrent neural network (RNN) to implement the control policy. In contrast to prevalent model-free methods, the learning approach proposed here takes advantage of the learned model and is more efficient. We use control barrier functions (CBFs) with the learned model to improve the safety of the system. We validate our algorithm via simulations and experiments. The results show that our approach can satisfy the given specification within very few system runs, and can be used for on-line control.