# LLMs-guided adaptive compensator: Bringing Adaptivity to Automatic Control Systems with Large Language Models

arXiv: https://arxiv.org/abs/2507.20509 · HTML: https://mlsanity.com/paper/2507.20509/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 28 Jul 2025.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 11 of 11)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [VIMA: General Robot Manipulation with Multimodal Prompts](https://mlsanity.com/paper/2210.03094/) (2022)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Large Language Models for Robotics: A Survey](https://mlsanity.com/paper/2311.07226/) (2023)
- [Vision-Language-Action (VLA) Models: Concepts, Progress, Applications and Challenges](https://mlsanity.com/paper/2505.04769/) (2025)
- [Capabilities of Large Language Models in Control Engineering: A Benchmark Study on GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra](https://mlsanity.com/paper/2404.03647/) (2024)
- [ControlAgent: Automating Control System Design via Novel Integration of LLM Agents and Domain Expertise](https://mlsanity.com/paper/2410.19811/) (2024)
- [Enhancing the LLM-Based Robot Manipulation Through Human-Robot Collaboration](https://mlsanity.com/paper/2406.14097/) (2024)
- [Safety-Critical Adaptive Control with Nonlinear Reference Model Systems](https://mlsanity.com/paper/1909.07916/) (2019)

## Abstract (arXiv)

With rapid advances in code generation, reasoning, and problem-solving, Large Language Models (LLMs) are increasingly applied in robotics. Most existing work focuses on high-level tasks such as task decomposition. A few studies have explored the use of LLMs in feedback controller design; however, these efforts are restricted to overly simplified systems, fixed-structure gain tuning, and lack real-world validation. To further investigate LLMs in automatic control, this work targets a key subfield: adaptive control. Inspired by the framework of model reference adaptive control (MRAC), we propose an LLM-guided adaptive compensator framework that avoids designing controllers from scratch. Instead, the LLMs are prompted using the discrepancies between an unknown system and a reference system to design a compensator that aligns the response of the unknown system with that of the reference, thereby achieving adaptivity. Experiments evaluate five methods: LLM-guided adaptive compensator, LLM-guided adaptive controller, indirect adaptive control, learning-based adaptive control, and MRAC, on soft and humanoid robots in both simulated and real-world environments. Results show that the LLM-guided adaptive compensator outperforms traditional adaptive controllers and significantly reduces reasoning complexity compared to the LLM-guided adaptive controller. The Lyapunov-based analysis and reasoning-path inspection demonstrate that the LLM-guided adaptive compensator enables a more structured design process by transforming mathematical derivation into a reasoning task, while exhibiting strong generalizability, adaptability, and robustness. This study opens a new direction for applying LLMs in the field of automatic control, offering greater deployability and practicality compared to vision-language models.