Evaluating LLMs as Interpretable Controllers for Dynamical Systems

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.