# Arithmetic-Geometric Mean Robustness for Control from Signal Temporal Logic Specifications

arXiv: https://arxiv.org/abs/1903.05186 · HTML: https://mlsanity.com/paper/1903.05186/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2019.

## Built on by (most cited first, 19 of 19)

- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [Learning Signal Temporal Logic through Neural Network for Interpretable Classification](https://mlsanity.com/paper/2210.01910/) (2022)
- [Safety of the Intended Driving Behavior Using Rulebooks](https://mlsanity.com/paper/2105.04472/) (2021)
- [STLCG++: A Masking Approach for Differentiable Signal Temporal Logic Specification](https://mlsanity.com/paper/2501.04194/) (2025)
- [Testing Rare Downstream Safety Violations via Upstream Adaptive Sampling of Perception Error Models](https://mlsanity.com/paper/2209.09674/) (2022)
- [Learning Robust and Correct Controllers from Signal Temporal Logic Specifications Using BarrierNet](https://mlsanity.com/paper/2304.06160/) (2023)
- [STL Robustness Risk over Discrete-Time Stochastic Processes](https://mlsanity.com/paper/2104.01503/) (2021)
- [Interpretable Fault Diagnosis of Rolling Element Bearings with Temporal Logic Neural Network](https://mlsanity.com/paper/2204.07579/) (2022)
- [STL-Based Synthesis of Feedback Controllers Using Reinforcement Learning](https://mlsanity.com/paper/2212.01022/) (2022)
- [Reinforcement Learning with Formal Performance Metrics for Quadcopter Attitude Control under Non-nominal Contexts](https://mlsanity.com/paper/2107.12942/) (2021)
- [Model Predictive Robustness of Signal Temporal Logic Predicates](https://mlsanity.com/paper/2209.07881/) (2022)
- [Neural Network-based Control for Multi-Agent Systems from Spatio-Temporal Specifications](https://mlsanity.com/paper/2104.02737/) (2021)
- [Neural Controller Synthesis for Signal Temporal Logic Specifications Using Encoder-Decoder Structured Networks](https://mlsanity.com/paper/2212.05200/) (2022)
- [Tolerance of Reinforcement Learning Controllers against Deviations in Cyber Physical Systems](https://mlsanity.com/paper/2406.17066/) (2024)
- [Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning](https://mlsanity.com/paper/2603.29868/) (2026)
- [Autonomous Vehicles Path Planning under Temporal Logic Specifications](https://mlsanity.com/paper/2410.07845/) (2024)
- [Feasibility-aware Learning of Robust Temporal Logic Controllers using BarrierNet](https://mlsanity.com/paper/2512.06973/) (2025)
- [GraSP-STL: A Graph-Based Framework for Zero-Shot Signal Temporal Logic Planning via Offline Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2603.29533/) (2026)
- [Reward Machines for Signal Temporal Logic](https://mlsanity.com/paper/2608.13625/) (2026)

## Abstract (arXiv)

We present a new average-based robustness score for Signal Temporal Logic (STL) and a framework for optimal control of a dynamical system under STL constraints. By averaging the scores of different specifications or subformulae at different time points, our new definition highlights the frequency of satisfaction, as well as how robustly each specification is satisfied at each time point. We show that this definition provides a better score for how well a specification is satisfied. Its usefulness in monitoring and control synthesis problems is illustrated through case studies.