# Capabilities of Large Language Models in Control Engineering: A Benchmark Study on GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra

arXiv: https://arxiv.org/abs/2404.03647 · HTML: https://mlsanity.com/paper/2404.03647/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 60 references that are in the map.
- First posted on arXiv 4 Apr 2024.

## Builds on (most cited first, 30 of 41)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Visual Instruction Tuning](https://mlsanity.com/paper/2304.08485/) (2023)
- [BLIP-2: Bootstrapping Language-Image Pre-training with Frozen Image Encoders and Large Language Models](https://mlsanity.com/paper/2301.12597/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [InstructBLIP: Towards General-purpose Vision-Language Models with Instruction Tuning](https://mlsanity.com/paper/2305.06500/) (2023)
- [MiniGPT-4: Enhancing Vision-Language Understanding with Advanced Large Language Models](https://mlsanity.com/paper/2304.10592/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [CodeGen: An Open Large Language Model for Code with Multi-Turn Program Synthesis](https://mlsanity.com/paper/2203.13474/) (2022)
- [Reasoning with Language Model is Planning with World Model](https://mlsanity.com/paper/2305.14992/) (2023)
- [Quantifying Language Models' Sensitivity to Spurious Features in Prompt Design or: How I learned to start worrying about prompt formatting](https://mlsanity.com/paper/2310.11324/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [VoxPoser: Composable 3D Value Maps for Robotic Manipulation with Language Models](https://mlsanity.com/paper/2307.05973/) (2023)
- [Large Language Models Can Self-Improve](https://mlsanity.com/paper/2210.11610/) (2022)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [LLM-Planner: Few-Shot Grounded Planning for Embodied Agents with Large Language Models](https://mlsanity.com/paper/2212.04088/) (2022)
- [Llemma: An Open Language Model For Mathematics](https://mlsanity.com/paper/2310.10631/) (2023)
- [A Systematic Evaluation of Large Language Models of Code](https://mlsanity.com/paper/2202.13169/) (2022)
- [On the Planning Abilities of Large Language Models : A Critical Investigation](https://mlsanity.com/paper/2305.15771/) (2023)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models](https://mlsanity.com/paper/2307.10635/) (2023)
- [ToolkenGPT: Augmenting Frozen Language Models with Massive Tools via Tool Embeddings](https://mlsanity.com/paper/2305.11554/) (2023)
- [MathPrompter: Mathematical Reasoning using Large Language Models](https://mlsanity.com/paper/2303.05398/) (2023)
- [Large Language Models as Commonsense Knowledge for Large-Scale Task Planning](https://mlsanity.com/paper/2305.14078/) (2023)

## Built on by (most cited first, 30 of 37)

- [Recent Advances in Large Langauge Model Benchmarks against Data Contamination: From Static to Dynamic Evaluation](https://mlsanity.com/paper/2502.17521/) (2025)
- [ControlAgent: Automating Control System Design via Novel Integration of LLM Agents and Domain Expertise](https://mlsanity.com/paper/2410.19811/) (2024)
- [MidiCaps: A large-scale MIDI dataset with text captions](https://mlsanity.com/paper/2406.02255/) (2024)
- [TSRBench: A Comprehensive Multi-task Multi-modal Time Series Reasoning Benchmark for Generalist Models](https://mlsanity.com/paper/2601.18744/) (2026)
- [Empirical Guidelines for Deploying LLMs onto Resource-constrained Edge Devices](https://mlsanity.com/paper/2406.03777/) (2024)
- [Frontier-Eng: Benchmarking Self-Evolving Agents on Real-World Engineering Tasks with Generative Optimization](https://mlsanity.com/paper/2604.12290/) (2026)
- [Benchmarking the Capabilities of Large Language Models in Transportation System Engineering: Accuracy, Consistency, and Reasoning Behaviors](https://mlsanity.com/paper/2408.08302/) (2024)
- [POT: Inducing Overthinking in LLMs via Black-Box Iterative Optimization](https://mlsanity.com/paper/2508.19277/) (2025)
- [Change Is the Only Constant: Dynamic LLM Slicing based on Layer Redundancy](https://mlsanity.com/paper/2411.03513/) (2024)
- [An Empirical Study of Group Conformity in Multi-Agent Systems](https://mlsanity.com/paper/2506.01332/) (2025)
- [EnviroExam: Benchmarking Environmental Science Knowledge of Large Language Models](https://mlsanity.com/paper/2405.11265/) (2024)
- [Securing Multi-turn Conversational Language Models From Distributed Backdoor Triggers](https://mlsanity.com/paper/2407.04151/) (2024)
- [SceneLLM: Implicit Language Reasoning in LLM for Dynamic Scene Graph Generation](https://mlsanity.com/paper/2412.11026/) (2024)
- [LLM-Agent-Controller: A Universal Multi-Agent Large Language Model System as a Control Engineer](https://mlsanity.com/paper/2505.19567/) (2025)
- [RLHF Fine-Tuning of LLMs for Alignment with Implicit User Feedback in Conversational Recommenders](https://mlsanity.com/paper/2508.05289/) (2025)
- [Exploring Vision Language Models for Facial Attribute Recognition: Emotion, Race, Gender, and Age](https://mlsanity.com/paper/2410.24148/) (2024)
- [MAPS: Multi-Agent Personality Shaping for Collaborative Reasoning](https://mlsanity.com/paper/2503.16905/) (2025)
- [PADBen: A Comprehensive Benchmark for Evaluating AI Text Detectors Against Paraphrase Attacks](https://mlsanity.com/paper/2511.00416/) (2025)
- [Topic Classification of Case Law Using a Large Language Model and a New Taxonomy for UK Law: AI Insights into Summary Judgment](https://mlsanity.com/paper/2405.12910/) (2024)
- [SmartLLMSentry: A Comprehensive LLM Based Smart Contract Vulnerability Detection Framework](https://mlsanity.com/paper/2411.19234/) (2024)
- [A Multimodal, Multilingual, and Multidimensional Pipeline for Fine-grained Crowdsourcing Earthquake Damage Evaluation](https://mlsanity.com/paper/2506.03360/) (2025)
- [Visual-Linguistic Agent: Towards Collaborative Contextual Object Reasoning](https://mlsanity.com/paper/2411.10252/) (2024)
- [The Lazy Student's Dream: ChatGPT Passing an Engineering Course on Its Own](https://mlsanity.com/paper/2503.05760/) (2025)
- [Symbolic Analysis of Grover Search Algorithm via Chain-of-Thought Reasoning and Quantum-Native Tokenization](https://mlsanity.com/paper/2505.04880/) (2025)
- [Difficulty Estimation and Simplification of French Text Using LLMs](https://mlsanity.com/paper/2407.18061/) (2024)
- [Can AI Master Construction Management (CM)? Benchmarking State-of-the-Art Large Language Models on CM Certification Exams](https://mlsanity.com/paper/2504.08779/) (2025)
- [Ensuring Ground Truth Accuracy in Healthcare with the EVINCE framework](https://mlsanity.com/paper/2405.15808/) (2024)
- [Unveiling LLM Mechanisms Through Neural ODEs and Control Theory](https://mlsanity.com/paper/2406.16985/) (2024)
- [TMIQ: Quantifying Test and Measurement Domain Intelligence in Large Language Models](https://mlsanity.com/paper/2503.02123/) (2025)
- [LLMs-guided adaptive compensator: Bringing Adaptivity to Automatic Control Systems with Large Language Models](https://mlsanity.com/paper/2507.20509/) (2025)

## Abstract (arXiv)

In this paper, we explore the capabilities of state-of-the-art large language models (LLMs) such as GPT-4, Claude 3 Opus, and Gemini 1.0 Ultra in solving undergraduate-level control problems. Controls provides an interesting case study for LLM reasoning due to its combination of mathematical theory and engineering design. We introduce ControlBench, a benchmark dataset tailored to reflect the breadth, depth, and complexity of classical control design. We use this dataset to study and evaluate the problem-solving abilities of these LLMs in the context of control engineering. We present evaluations conducted by a panel of human experts, providing insights into the accuracy, reasoning, and explanatory prowess of LLMs in control engineering. Our analysis reveals the strengths and limitations of each LLM in the context of classical control, and our results imply that Claude 3 Opus has become the state-of-the-art LLM for solving undergraduate control problems. Our study serves as an initial step towards the broader goal of employing artificial general intelligence in control engineering.