Large Language Models in the Loop: A Stability- and Network-Aware Survey in Networked Control, Cyber-Physical, and Multi-Agent Systems

Recent literature shows that large language models (LLMs) are useful for general-purpose tasks yet perform poorly on specific domain ones. One reason is the difficulty of supplying narrow context to a general-purpose model and of bounding the task it is asked to perform. It is possible to hypothesise that a multi-agent reformulation under process-control principles offers a route to address those points, since control theory provides a discipline of decomposing a system into elements of contained scope, each defending one controlled variable, with conflicts resolved by structural priority: MIN/MAX selector networks for CV-CV switching and split-range (split-parallel) logic for MV-MV switching. The present work proposes such a reformulation, derived from Advanced Regulatory Control (ARC) theory. Each feedback loop in the ARC chain is mapped to one specialised LLM operator agent carrying the loop's control-theoretic context (controlled variable, setpoint, chain priority, selector kind). The chain's interaction logic (MIN/MAX selectors, override paths) is encapsulated as a single orchestrator agent. Two orchestrator variants are tested: a deterministic rule chain, and a Claude-based LLM orchestrator at a slower tier. The control principles limit each agent's task and inform how its limitations are handled. The multi-agent system inherits the safety property of the ARC chain: every constraint conflict is resolved deterministically by the orchestrator, regardless of the LLM output. Evaluated on a dairy-barn ventilation case over a 4-day mixed-season scenario, Qwen 2.5 7B Instruct operator agents running offline on a 24 GB consumer GPU at a 5-minute cadence produce auditable trajectories, each paired with an operator-voice rationale that supports a control campaign logbook.

Large Language Models (LLMs), deep learning architectures with typically over 10 billion parameters, have recently begun to be integrated into various cyber-physical systems (CPS) such as robotics, industrial automation, and autopilot systems. The abstract knowledge and reasoning capabilities of LLMs are employed for tasks like planning and navigation. However, a significant challenge arises from the tendency of LLMs to produce "hallucinations" - outputs that are coherent yet factually incorrect or contextually unsuitable. This characteristic can lead to undesirable or unsafe actions in the CPS. Therefore, our research focuses on assuring the LLM-enabled CPS by enhancing their critical properties. We propose SafePilot, a novel hierarchical neuro-symbolic framework that provides end-to-end assurance for LLM-enabled CPS according to attribute-based and temporal specifications. Given a task and its specification, SafePilot first invokes a hierarchical planner with a discriminator that assesses task complexity. If the task is deemed manageable, it is passed directly to an LLM-based task planner with built-in verification. Otherwise, the hierarchical planner applies a divide-and-conquer strategy, decomposing the task into sub-tasks, each of which is individually planned and later merged into a final solution. The LLM-based task planner translates natural language constraints into formal specifications and verifies the LLM's output against them. If violations are detected, it identifies the flaw, adjusts the prompt accordingly, and re-invokes the LLM. This iterative process continues until a valid plan is produced or a predefined limit is reached. Our framework supports LLM-enabled CPS with both attribute-based and temporal constraints. Its effectiveness and adaptability are demonstrated through two illustrative case studies.

Multi-agent large language model (LLM) systems often rely on verifier and critic agents to suppress hallucinations, but verification is delayed. During this delay, false claims can propagate through the agent network. We model this process as delayed consensus on a graph with grounded corrector nodes. Spectral decomposition by the grounded Laplacian yields a closed-form stability threshold for the verification dose: correction that is too strong or too delayed can turn consensus into oscillation. The most unstable regime occurs when the communication and verification delays coincide; for delay two, the threshold is the inverse golden ratio. The same framework gives a supermodular placement objective and a greedy (1-1/e)-approximation rule for assigning a limited corrector budget to influential nodes. Experiments across five open models confirm the predicted dose-delay oscillations. By contrast, grounded factual answering makes truth an absorbing boundary and eliminates the effect, suggesting that the instability is specific to signed-belief tasks while grounded verification remains stabilizing