Structure from Reasoning, Numbers from Search: On-Premise Open LLMs as Structural Priors for Coupled MIMO Controller Tuning

Problem
Tuning controllers for strongly coupled multi-input multi-output (MIMO) systems presents significant challenges due to the complexities of loop interactions and non-convex cost landscapes. Traditional decentralized auto-tuning methods often overlook these interactions, while local numerical optimization techniques can stall. This paper addresses the gap in the literature regarding the application of on-premise open-source large language models (LLMs) for controller tuning, particularly in scenarios where plant models are unavailable. The authors present a preprint work that investigates the potential of LLMs to serve as structural priors in this context.

Method
The authors propose a scaffolded open LLM that reasons about the coupling in MIMO systems and suggests an asymmetric control structure. The tuning process is evaluated on two test cases: a single-loop continuous stirred-tank reactor (CSTR) and a strongly coupled quadruple-tank system. The performance is measured using a penalized cost function ( J = \text{IAE} + \lambda \cdot \text{TV}(u) ), which balances tracking performance with actuator chattering. The LLM’s tuning is compared against classical relay-feedback tuning and local optimization methods. The LLM is trained to provide structural insights rather than direct optimization, leading to a proposed control structure that is refined using classical optimization techniques.

Results
In the single-loop CSTR scenario, classical relay-feedback tuning achieved an Integral of Absolute Error (IAE) of 0.106, outperforming the LLM tuner at 0.162. However, in the quadruple-tank system, naive relay tuning and naive LLM tuning both performed poorly (J ~ 28.6 and 29.7, respectively), while open-loop control yielded a better score of 22.7. The scaffolded LLM, however, proposed an effective asymmetric structure, achieving J ~ 16.9 ± 0.2 from any initialization. When refined with a classical optimizer, the performance improved to J ~ 12.0, with a success rate of 10/10 runs, compared to 0/10 for local optimization. The LLM demonstrated sample efficiency, requiring only 18 evaluations to produce a usable controller, while a global optimizer (differential evolution) performed worse than open-loop control in the same context.

Limitations
The authors note that the LLM’s advantages are context-dependent, as it did not provide benefits in simpler or benign plant scenarios. Additionally, the reliance on a scaffolded approach may limit the generalizability of the findings. The paper does not explore the scalability of the LLM approach beyond the tested configurations, nor does it address potential computational overhead associated with LLM deployment.

Why it matters
This work highlights the potential of on-premise LLMs as structural priors in control tuning, emphasizing their sample efficiency and interpretability over traditional optimization methods. The findings delineate the conditions under which LLMs can enhance control strategies, providing a reproducible benchmark for future research in this area. This research contributes to the growing intersection of machine learning and control theory, as discussed in arXiv.