# Control from Signal Temporal Logic Specifications with Smooth Cumulative Quantitative Semantics

arXiv: https://arxiv.org/abs/1904.11611 · HTML: https://mlsanity.com/paper/1904.11611/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2019.

## Built on by (most cited first, 16 of 16)

- [Learning Model Checking and the Kernel Trick for Signal Temporal Logic on Stochastic Processes](https://mlsanity.com/paper/2201.09928/) (2022)
- [Testing Rare Downstream Safety Violations via Upstream Adaptive Sampling of Perception Error Models](https://mlsanity.com/paper/2209.09674/) (2022)
- [STL Robustness Risk over Discrete-Time Stochastic Processes](https://mlsanity.com/paper/2104.01503/) (2021)
- [Safe Model-based Control from Signal Temporal Logic Specifications Using Recurrent Neural Networks](https://mlsanity.com/paper/2103.15938/) (2021)
- [Reinforcement Learning with Formal Performance Metrics for Quadcopter Attitude Control under Non-nominal Contexts](https://mlsanity.com/paper/2107.12942/) (2021)
- [Interpretable Imitation Learning via Generative Adversarial STL Inference and Control](https://mlsanity.com/paper/2402.10310/) (2024)
- [Neural Network-based Control for Multi-Agent Systems from Spatio-Temporal Specifications](https://mlsanity.com/paper/2104.02737/) (2021)
- [Learning Spatio-Temporal Specifications for Dynamical Systems](https://mlsanity.com/paper/2112.10714/) (2021)
- [Neural Controller Synthesis for Signal Temporal Logic Specifications Using Encoder-Decoder Structured Networks](https://mlsanity.com/paper/2212.05200/) (2022)
- [Signal Temporal Logic-Guided Apprenticeship Learning](https://mlsanity.com/paper/2311.05084/) (2023)
- [Tolerance of Reinforcement Learning Controllers against Deviations in Cyber Physical Systems](https://mlsanity.com/paper/2406.17066/) (2024)
- [STL-based Optimization of Biomolecular Neural Networks for Regression and Control](https://mlsanity.com/paper/2509.05481/) (2025)
- [Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning](https://mlsanity.com/paper/2603.29868/) (2026)
- [Learning-enabled Parameter Synthesis for Nonlinear Systems from Signal Temporal Logic](https://mlsanity.com/paper/2607.08899/) (2026)
- [Reward Machines for Signal Temporal Logic](https://mlsanity.com/paper/2608.13625/) (2026)
- [PAA: The Probabilistic Allen Algebra: A Generative and Complete Probabilistic Extension of Allen's Interval Relations](https://mlsanity.com/paper/2609.20634/) (2026)

## Abstract (arXiv)

We present a framework to synthesize control policies for nonlinear dynamical systems from complex temporal constraints specified in a rich temporal logic called Signal Temporal Logic (STL). We propose a novel smooth and differentiable STL quantitative semantics called cumulative robustness, and efficiently compute control policies through a series of smooth optimization problems that are solved using gradient ascent algorithms. Furthermore, we demonstrate how these techniques can be incorporated in a model predictive control framework in order to synthesize control policies over long time horizons. The advantages of combining the cumulative robustness function with smooth optimization methods as well as model predictive control are illustrated in case studies.