# Evaluating LLMs as Interpretable Controllers for Dynamical Systems

arXiv: https://arxiv.org/abs/2607.22609 · HTML: https://mlsanity.com/paper/2607.22609/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 21 references that are in the map.
- First posted on arXiv 14 Jun 2026.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Large Language Models Encode Clinical Knowledge](https://mlsanity.com/paper/2212.13138/) (2022)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Inner Monologue: Embodied Reasoning through Planning with Language Models](https://mlsanity.com/paper/2207.05608/) (2022)
- [Language Models as Zero-Shot Planners: Extracting Actionable Knowledge for Embodied Agents](https://mlsanity.com/paper/2201.07207/) (2022)
- [LLM-Planner: Few-Shot Grounded Planning for Embodied Agents with Large Language Models](https://mlsanity.com/paper/2212.04088/) (2022)
- [Large Language Models for Robotics: Opportunities, Challenges, and Perspectives](https://mlsanity.com/paper/2401.04334/) (2024)
- [Learning to Model the World with Language](https://mlsanity.com/paper/2308.01399/) (2023)
- [Language Instructed Reinforcement Learning for Human-AI Coordination](https://mlsanity.com/paper/2304.07297/) (2023)
- [Problematic Tokens: Tokenizer Bias in Large Language Models](https://mlsanity.com/paper/2406.11214/) (2024)
- [Large Language Models for Control](https://mlsanity.com/paper/2511.00337/) (2025)
- [Hybrid Modeling, Sim-to-Real Reinforcement Learning, and Large Language Model Driven Control for Digital Twins](https://mlsanity.com/paper/2510.23882/) (2025)

## Abstract (arXiv)

Large Language Models (LLMs) are increasingly used for decision-making and reasoning tasks, yet their potential as controllers for physical systems remains largely unexplored. This work investigates whether LLMs can function as interpretable controllers for a dynamic thermal environment, examining their ability to follow setpoints, interpret natural-language commands, reason about actuator effects, and incorporate prior model-based knowledge. Five LLMs of varying scales are evaluated under multiple scenarios, including settings with penalties on heater or fan usage and cases where the models have access to a physics-based prediction tool. The results show that control performance depends on model complexity: while low- and mid-scale models frequently misinterpret actuator dynamics or generate inconsistent reasoning, high-complexity models such as Qwen-3~14B and GPT-4o achieve accurate temperature tracking, stable actuator usage, and coherent explanations aligned with physical principles. Incorporating a physics-based model significantly improves control smoothness and energy efficiency by enabling anticipatory decision-making. A detailed reasoning taxonomy further reveals a clear progression from causal misinterpretation in smaller models to cohesive and temporally aware reasoning in larger ones. The findings demonstrate that LLMs can act as interpretable controllers when sufficiently capable and appropriately grounded in domain knowledge, highlighting promising opportunities for hybrid model-based and language-driven control strategies that can provide plausible explanations.