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

-- 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 LLMs-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 LLMs-guided adaptive com-pensator outperforms traditional adaptive controllers and significantly reduces reasoning complexity compared to the LLMs-guided adaptive controller. The Lyapunov-based analysis and reasoning-path inspection demonstrate that the LLMs-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.