# Model-Based Reinforcement Learning for Approximate Optimal Control with Temporal Logic Specifications

arXiv: https://arxiv.org/abs/2101.07156 · HTML: https://mlsanity.com/paper/2101.07156/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2021.

## Built on by (most cited first, 5 of 5)

- [Signal Temporal Logic Neural Predictive Control](https://mlsanity.com/paper/2309.05131/) (2023)
- [Temporal Logic Specification-Conditioned Decision Transformer for Offline Safe Reinforcement Learning](https://mlsanity.com/paper/2402.17217/) (2024)
- [Modeling Risk in Reinforcement Learning: A Literature Mapping](https://mlsanity.com/paper/2312.05231/) (2023)
- [About Time: Model-free Reinforcement Learning with Timed Reward Machines](https://mlsanity.com/paper/2512.17637/) (2025)
- [Efficient Bayes-Adaptive Reinforcement Learning with Temporal Logic Specifications](https://mlsanity.com/paper/2609.20954/) (2026)

## Abstract (arXiv)

In this paper we study the problem of synthesizing optimal control policies for uncertain continuous-time nonlinear systems from syntactically co-safe linear temporal logic (scLTL) formulas. We formulate this problem as a sequence of reach-avoid optimal control sub-problems. We show that the resulting hybrid optimal control policy guarantees the satisfaction of a given scLTL formula by constructing a barrier certificate. Since solving each optimal control problem may be computationally intractable, we take a learning-based approach to approximately solve this sequence of optimal control problems online without requiring full knowledge of the system dynamics. Using Lyapunov-based tools, we develop sufficient conditions under which our approximate solution maintains correctness. Finally, we demonstrate the efficacy of the developed method with a numerical example.