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

Haiping Du, Linping Chan

arXiv:2609.16599v1eess.SYcs.AIcs.SY

TL;DR

Safety-critical networked, cyber-physical, and multi-agent systems require guarantees that stochastic, slow LLMs do not inherently provide. This survey frames LLMs as supervisory agents over fast control layers and synthesizes deployments across these domains. It finds that formal stability analysis built on bounded LLM-error characterization remains a central open challenge.

  • Problem

    The survey asks how LLMs can enter networked control loops without compromising the stability and safety guarantees required in safety-critical systems.

    Source: §1.2 · p. 2

  • Method

    The survey frames the LLM as a slow supervisor that configures goals and controller parameters while a certified inner loop enforces closed-loop stability.

    Source: §2.2 · p. 6, §4.1 · p. 10

  • Results

    Across autonomous driving, networking and network operations, and CPSs, LLMs are assigned supervisory roles, while bounded LLM-error characterization and formal stability analysis remain open challenges.

    Source: §6.4 · p. 25

  • Takeaways & Limitations

    The survey treats LLM-in-the-loop operation as a networked control problem to which classical control tools transfer.

    Source: §6.4 · p. 24

    Surveyed NCS research remains overwhelmingly operations-oriented, with almost no formal stability analysis for the resulting closed loop.

    Source: §5.1 · p. 16

Abstract

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Modern networked control systems (NCSs), cyber-physical systems (CPSs), and complex multi-agent network systems (CNSs) increasingly rely on large language models (LLMs) for high-level decision-making. However, the slow, stochastic nature of LLMs directly conflicts with the strict stability and safety guarantees required by these physical systems. This survey presents a unified analysis of how LLMs can be admitted into the control loop of NCS, CPS, and CNS without compromising closed-loop guarantees. We organize this around a core principle: the LLM operates as a slow supervisor adjusting high-level goals and constraints, while a fast, certified inner loop maintains physical stability. Under this framework, LLM integration maps directly to classical networked control challenges, where inference latency acts as delay, API failures as packet dropouts, tokenization as quantization, and hallucinations as bounded disturbances. We assess current developments across all these three domains, highlighting that rising model capabilities are frequently accompanied by a drop in formal safety assurances. Finally, we propose concrete future research directions, identifying the widespread lack of formal stability proofs as the field's central open problem.

1. Introduction

LLMs bring semantic planning and coordination to networked physical systems, but their latency and stochastic outputs conflict with established stability and safety requirements. The survey unifies these domains around supervisory LLMs, fast control layers, and a review of the field’s methods and open gaps.

1.1 Background and Motivation

  • NCSs, CPSs, and CNSs share coupled dynamics communicating over uncertain networks, while LLMs add semantic planning and coordination above classical control loops.The survey asks how LLMs can join these systems without compromising stability and safety.Source: §1.1 · pp. 1–2, §1.2 · p. 2

1.2 Problem Statement and Scope

  • LLMs’ stochastic outputs, high latency, and lack of native stability properties conflict with safety-critical systems’ rigorous guarantees.The survey focuses on engineered multi-agent systems and includes multimodal and embodied foundation models alongside LLMs.Source: §1.2 · p. 2

1.3 Related Surveys and Positioning

  • Existing surveys do not combine analysis of LLMs inside networked dynamical systems, formal stability and safety guarantees, and coverage of NCS, CPS, and CNS.The survey positions itself against domain-specific work that omits one or more of these dimensions.Source: §1.3 · pp. 2–3

1.4 Contributions

  • The proposed architecture places LLM supervisory reasoning alongside certificate-based safety filters to guide lower-level physical and networked control loops.It models latency as delay, API timeouts as dropouts, token decoding as quantization, and hallucinations as bounded disturbances.Source: §1.4 · pp. 3–5
  • The survey classifies methods by intelligence, verification, network awareness, loop role, and timescale, then synthesizes deployments across NCS, CPS, and CNS.Its safety toolbox includes runtime filters, control barrier functions, conformal prediction, and verification certificates; it identifies missing Lyapunov-based stability proofs as a primary gap.Source: §1.4 · p. 5

1.5 Methodology and Organization

  • The structured review focuses on literature published primarily from 2021 to 2026 and makes no claim of exhaustiveness.It spans control, robotics, machine learning, and systems venues.Source: §1.5 · p. 5

2. A Unified Networked Model

The survey models networked systems with a common dynamical framework and places the LLM in a slower supervisory loop that changes control parameters. It connects LLM-specific failure modes to familiar network-control problems and asks whether the fast control layer preserves safety and stability.

2.1 General Networked Dynamical Model

  • A shared model represents N interconnected subsystems with local dynamics, control inputs, graph-based coupling, and disturbances, with diffusive coupling reducible to a Laplacian term.Network sensing and actuation may involve delay and loss, while local controllers use networked neighbor-state estimates.Source: §2.1 · pp. 5–6

2.2 The LLM as a System Component

  • The LLM generates supervisory parameters from subsystem data and context, which are held between sparse, aperiodic invocations in a slow outer loop around a continuous fast controller.Parameters can represent references, constraints, triggering thresholds, gains, modes, or network coupling weights.Source: §2.2 · p. 6
  • Stochastic, discrete, and fallible LLM outputs are modeled as parameter variation and bounded error; under stated assumptions, an ISS nominal loop inherits practical or stochastic stability with an ultimate bound tied to error and invocation interval.This is a design template, not a theorem; individual methods require their own assumptions.Source: §2.2 · pp. 6–7

2.3 The LLM in the Loop as a Networked-Control Problem

  • Inference latency, failed calls, token decoding, and hallucinations map respectively to delay, dropout, quantization, and bounded disturbance, allowing classical control tools to analyze these effects,.On a failed call, the zero-order hold retains the prior parameter; latency also means the output uses earlier state data.Source: §2.2 · p. 6, §2.3 · p. 7, Table 2 · p. 7
  • Across NCS, CPS, and CNS, the supervisory parameter represents scheduling or triggering decisions, physical-system references or constraints, or network coupling and topology, respectively.The LLM's admissibility depends on preserving the underlying control-layer safety and stability guarantees.Source: §2.3 · pp. 7–8, Table 3 · p. 8

3. Analytical Foundations

This section assembles selected control-theoretic tools for analyzing stability, safety, and aperiodic LLM invocation, then distinguishes LLMs from classical learning-based control. The tools connect bounded LLM errors and supervisory updates to formal guarantees, while the comparison highlights assumptions conventional learning-based analyses rely on.

3. Analytical Foundations

  • The section provides targeted foundations for the later framework, treating LLM error as an exogenous disturbance and invocation as aperiodic sampling.The selected tools are intended to support formal stability and safety statements, not to survey control theory or machine learning broadly.Source: §3 · p. 8, §3.1 · p. 8

3.1.1 Lyapunov stability and ISS

  • Input-to-state stability bounds state response by decay from the initial condition plus a gain on disturbance magnitude, so bounded LLM parameter error yields bounded ultimate error in an ISS nominal loop.With no disturbance, the ISS-Lyapunov condition reduces to the standard asymptotic-stability condition.Source: §3.1.1 · pp. 8–9

3.1.2 Network stability: consensus and synchronization

  • For coupled systems, consensus and synchronization depend on graph-Laplacian spectrum, particularly algebraic connectivity, which governs convergence rate and is affected by changes to coupling weights or topology.For the linear consensus protocol, the rate is set by the second-smallest Laplacian eigenvalue.Source: §3.1.2 · p. 9

3.1.3 Event- and self-triggered control

  • Event- and self-triggered control schedules sensing and actuation when state error crosses a threshold, yielding aperiodic invocation times and holding the input constant between events.This can limit sensing and expensive LLM computations to times when state drift exceeds tolerated bounds.Source: §3.1.3 · p. 9

3.1.4 Safety certificates: CBFs

  • A control barrier function defines conditions for a safe set to remain forward-invariant, and its safety filter minimally adjusts a nominal input to satisfy those conditions.The filter is intended to override or adjust LLM-generated commands before actuation.Source: §3.1.4 · p. 9

3.2 The LLM Perspective

  • Classical learning-based control embeds learned components in the loop and addresses uncertainty or constraints, whereas LLMs use semantic representations at supervisory timescales without inherent boundedness or Lipschitz assumptions.Learning-based MPC provides a comparison point for LLM parameterization, but retains formal guarantees that the survey says LLM formulations relinquish.Source: §3.2 · pp. 9–10

4. A Stability–Safety–Intelligence Framework

The framework places the LLM above a certified fast control loop, organizing integration by operational role and the guarantees that survive. As coupling to the fast loop increases, theoretical guarantees weaken; safety mechanisms bound or filter LLM error before it reaches the plant.

4.1 Structure and Taxonomy

  • Four pathways—interpreter or estimator, supervisor, planner or coordinator, and in-loop policy—order LLM integration from least to greatest coupling with the fast control loop.The architecture comprises the plant, a feedback controller, and an LLM module; tighter coupling corresponds to weaker theoretical guarantees.Source: §4.1 · p. 10
  • The five-dimensional taxonomy centers on the LLM's role and inference timescale, which predict the formal guarantee across the illustrated systems.LLM4PLC operates offline with proof-level guarantees, SayCan at seconds-scale with runtime assurance, and RT-2 at sub-second scale with essentially no formal guarantees.Source: §4.1 · p. 11

4.2 LLM-Specific Method Categories

  • Category A uses offline LLM-generated artifacts verified before deployment, preserving classical stability and safety frameworks and offering the strongest guarantees.Examples include verified controller code and formal-planner inputs.Source: §4.2 · p. 12
  • Category B uses the LLM to set parameters while a certified inner loop maintains physical stability, with proposed updates passing through formal filters.The survey presents this as the current deployment trade-off between semantic performance and formal guarantees.Source: §4.2 · p. 12
  • Category C lets LLMs or VLA models drive actions directly, offering the weakest inherent guarantees and requiring external safety enforcement.A safety chip can veto actions that violate user-specified temporal-logic constraints.Source: §4.2 · pp. 12–13

4.3 Safety Mechanisms and the Perturbation View

  • The stability template yields practical stability when the nominal loop is ISS and LLM execution error is bounded; its ultimate bound scales with error and inter-invocation interval.The survey presents this as a design template, not a theorem, with assumptions varying by method.Source: §4.3 · pp. 13–14
  • Safety mechanisms include nominal stability certificates, probabilistic bounds on LLM uncertainty, runtime safety filters, and mathematical or logical output validation.These mechanisms bound or filter LLM errors before they affect the plant.Source: §4.3 · p. 14

5. LLMs Across NCS, CPS, and CNS

Across NCS, CPS, and CNS, the survey examines where LLMs sit in the control loop, what they generate, and which classical guarantees are preserved. The applications range from supervisory network operations to embodied control and multi-agent coordination.

5.1 LLMs in NCS

  • NCS LLMs handle configuration, diagnosis, and intent translation above the millisecond path, but surveyed work offers almost no formal closed-loop stability analysis.The section identifies co-design with event- and self-triggered mechanisms and standardized closed-loop benchmarks as research needs.Source: §5.1 · pp. 15–16

5.2 LLMs in CPS

  • CPS applications span hierarchical robotics, driving, and infrastructure control, but in-loop models sharpen the tension between intelligence and guarantees, making certified pre-actuation safeguards central.The survey also calls for stability-aware closed-loop benchmarks and analysis of LLM-triggered mode changes.Source: §5.2 · pp. 17–18

5.3 LLMs in CNS

  • CNS LLMs coordinate swarms, fleets, and network controllers, yet collective stability is rarely certified and semantic consensus, message quantization, and distributed safety remain open.The agenda also includes scalable coordination whose convergence can be analyzed as the agent count grows.Source: §5.3 · pp. 19–20

5.4 Network-Level Perspective

  • Across domains, topology and coupling govern collective behavior, so LLM-driven references, weights, or topology must preserve network-level guarantees despite slow, fallible modulation.The survey frames LLM-aware guarantees as treating language-driven agents as bounded, filterable graph perturbations.Source: §5.4 · p. 20

6. Open Challenges, Future Directions, and Conclusion

Across LLM-in-the-loop domains, theoretical obstacles center on unbounded model error and missing formal guarantees, while practical barriers include latency, evaluation, security, and interpretability. The survey concludes that LLMs remain supervisors over guaranteed control layers and outlines four directions for safer integration.

6.1 Theoretical Challenges

  • Hallucinations act as uncharacterized control-loop disturbances, and weak continuous-signal and temporal reasoning plus unscalable verification leave LLM-in-the-loop systems largely without Lyapunov- or ISS-based analyses.Current methods do not provide the uniform error bounds required by the survey’s ISS template.Source: §6.1 · pp. 21–22

6.2 Practical Challenges

  • Practical deployment is constrained by inference latency and hardware limits, scarce corner-case data and unsettled evaluation, alongside security, privacy, and interpretability concerns.Existing benchmarks do not score closed-loop stability under LLM-induced perturbation.Source: §6.2 · pp. 22–23

6.3 Future Directions

  • Synchronous validation environments and digital twins could test LLM proposals against plant dynamics and constraints, returning counterexamples before commands reach the physical layer.The survey also cites runtime anomaly detection and safety-specification enforcement as complementary tools.Source: §6.3 · pp. 23–24
  • The survey proposes assembling runtime filters, barrier functions, reachability, certificates, and conformal verification into an LLM-admitting architecture with an end-to-end formal guarantee.The open challenge is integration of these mechanisms, rather than inventing individual safety tools.Source: §6.3 · p. 24
  • Autonomous tool-using multi-agent systems could coordinate at CNS scale through solvers, verifiers, and simulators, but standardized control-competence benchmarks remain necessary.Representing tools as discrete tokens is one proposal for reducing tool-use overhead.Source: §6.3 · p. 24
  • Moving LLM-derived policies closer to the inner loop requires real-time-capable models, verified or filter-wrapped policies, and bounded-error characterization.The survey keeps stability guarantees with a fast certified element such as a safety filter.Source: §6.3 · p. 24

6.4 Conclusion

  • Across autonomous driving, networking, and CPSs, surveyed systems use LLMs as supervisors, while bounded error characterization and formal stability analysis remain the shared open challenge.The survey identifies closing this gap as necessary to move from experimental demonstrations toward safety-critical deployments.Source: §6.4 · p. 25
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