# Robust Temporal Logic Model Predictive Control

arXiv: https://arxiv.org/abs/1511.00347 · HTML: https://mlsanity.com/paper/1511.00347/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2015.

## Built on by (most cited first, 21 of 21)

- [A Survey of Optimization-based Task and Motion Planning: From Classical To Learning Approaches](https://mlsanity.com/paper/2404.02817/) (2024)
- [TeLoGraF: Temporal Logic Planning via Graph-encoded Flow Matching](https://mlsanity.com/paper/2505.00562/) (2025)
- [Risk Verification of Stochastic Systems with Neural Network Controllers](https://mlsanity.com/paper/2209.09881/) (2022)
- [Learning Robust and Correct Controllers from Signal Temporal Logic Specifications Using BarrierNet](https://mlsanity.com/paper/2304.06160/) (2023)
- [Zero-Shot Trajectory Planning for Signal Temporal Logic Tasks](https://mlsanity.com/paper/2501.13457/) (2025)
- [Guiding Multi-agent Multi-task Reinforcement Learning by a Hierarchical Framework with Logical Reward Shaping](https://mlsanity.com/paper/2411.01184/) (2024)
- [Safe Model-based Control from Signal Temporal Logic Specifications Using Recurrent Neural Networks](https://mlsanity.com/paper/2103.15938/) (2021)
- [Interpretable Imitation Learning via Generative Adversarial STL Inference and Control](https://mlsanity.com/paper/2402.10310/) (2024)
- [Traffic-Rule-Compliant Trajectory Repair via Satisfiability Modulo Theories and Reachability Analysis](https://mlsanity.com/paper/2412.15837/) (2024)
- [Inferring Temporal Logic Properties from Data using Boosted Decision Trees](https://mlsanity.com/paper/2105.11508/) (2021)
- [STeP: Signal Temporal Logic for Precise Specifications for Action Generation with Vision Language Models](https://mlsanity.com/paper/2607.18580/) (2026)
- [Neural Controller Synthesis for Signal Temporal Logic Specifications Using Encoder-Decoder Structured Networks](https://mlsanity.com/paper/2212.05200/) (2022)
- [Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning](https://mlsanity.com/paper/2603.29868/) (2026)
- [Reinforcement Learning Agent Training with Goals for Real World Tasks](https://mlsanity.com/paper/2107.10390/) (2021)
- [CatlNet: Learning Communication and Coordination Policies from CaTL+ Specifications](https://mlsanity.com/paper/2212.11792/) (2022)
- [Scaling Learning based Policy Optimization for Temporal Logic Tasks by Controller Network Dropout](https://mlsanity.com/paper/2403.15826/) (2024)
- [Safety Verification and Navigation for Autonomous Vehicles based on Signal Temporal Logic Constraints](https://mlsanity.com/paper/2409.10689/) (2024)
- [Feasibility-aware Learning of Robust Temporal Logic Controllers using BarrierNet](https://mlsanity.com/paper/2512.06973/) (2025)
- [Specification-Aware Distribution Shaping for Robotics Foundation Models](https://mlsanity.com/paper/2603.17969/) (2026)
- [Zero-Shot Signal Temporal Logic Planning with Disjunctive Branch Selection in Dynamic Semantic Maps](https://mlsanity.com/paper/2605.01222/) (2026)
- [Logic-VLA: A Temporal Logic Conditioned Vision-Language-Action Model](https://mlsanity.com/paper/2608.20556/) (2026)

## Abstract (arXiv)

Control synthesis from temporal logic specifications has gained popularity in recent years. In this paper, we use a model predictive approach to control discrete time linear systems with additive bounded disturbances subject to constraints given as formulas of signal temporal logic (STL). We introduce a (conservative) computationally efficient framework to synthesize control strategies based on mixed integer programs. The designed controllers satisfy the temporal logic requirements, are robust to all possible realizations of the disturbances, and optimal with respect to a cost function. In case the temporal logic constraint is infeasible, the controller satisfies a relaxed, minimally violating constraint. An illustrative case study is included.