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arxiv: 2602.03433 · v1 · pith:6CDR5A3Znew · submitted 2026-02-03 · 📡 eess.SY · cs.SY

When control meets large language models: From words to dynamics

Komeil Nosrati , Aleksei Tepljakov , Juri Belikov , Eduard Petlenkov This is my paper

Pith reviewed 2026-05-21 14:46 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords large language modelscontrol theoryprompt designsystem dynamicsalignmentinterpretabilitystate-space frameworkbidirectional continuum
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The pith

Large language models and control theory form a bidirectional continuum from prompt design to system dynamics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper sets out to establish that LLMs and control theory are connected in both directions, so that language models can help build and improve control systems while control ideas can be used to guide and stabilize LLM behavior. A reader would care because this framing could make AI tools more useful in engineering tasks like controller design and make the models themselves more reliable and understandable for real-world use. It maps how LLMs assist control work directly through design help and indirectly through research support. It then shows control methods improving LLMs via input changes, parameter edits, and activation tweaks. Finally it treats the models as state-space systems tied to external loops and flags open challenges for future work.

Core claim

The paper claims that the interconnection between LLMs and control theory is best understood as a bidirectional continuum running from prompt design to full system dynamics. LLMs advance control directly by assisting in controller design and synthesis and indirectly by augmenting research workflows. Control concepts in turn steer LLM trajectories away from undesired outputs, improving reachability and alignment through input optimization, parameter editing, and activation-level interventions. Deeper integration comes from viewing LLMs as dynamic systems in a state-space framework whose internal states connect to external control loops. The goal is to develop LLMs that are as interpretable, (

What carries the argument

The bidirectional continuum linking prompt design to system dynamics, in which prompts aid control synthesis while control methods optimize LLM inputs, parameters, and activations.

Load-bearing premise

That control-theoretic interventions such as input optimization and activation changes can steer LLM behavior without degrading core language performance or creating new instabilities.

What would settle it

A controlled test in which applying input optimization or activation interventions to a standard LLM produces no measurable gain in alignment metrics or causes a clear drop in language task accuracy would falsify the claimed benefits.

Figures

Figures reproduced from arXiv: 2602.03433 by Aleksei Tepljakov, Eduard Petlenkov, Juri Belikov, Komeil Nosrati.

Figure 1
Figure 1. Figure 1: Capabilities of LLMS. paradigm based on next-token prediction [8]. The latter combines both approaches, unifying NLP tasks under a text-to-text framework and enabling flexible sequence-to￾sequence modeling for both comprehension and genera￾tion [9]. Building upon these foundations, the GPT family developed by OpenAI pioneered large-scale self-supervised pre-training [10], enabling strong zero- and few-shot… view at source ↗
Figure 2
Figure 2. Figure 2: Conceptual map of three key intersections between control and LLMs. • What are challenges and future trends at this intersection? By addressing these questions, we aim to provide a struc￾tured understanding of this rapidly developing field and motivate future work at the convergence of dynamical mod￾eling, control theory, and LLMs. While we have already examined why this intersection matters and will conti… view at source ↗
Figure 3
Figure 3. Figure 3: Stanford Cart on an obstacle course with a young H. Moravec (1977) [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: When control meets LLMs: A timeline. feedback-driven approaches (see [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The early RLHF pipeline. had unified insights from psychology, optimal control, and temporal-difference learning, establishing RL as a distinct discipline. Conceptually, RL is grounded in control-theoretic frameworks such as Markov decision processes (MDPs), paralleling optimal control, where an agent seeks to mini￾mize cumulative cost or maximize reward. A key milestone was Q-learning (Watkins, 1989 [53];… view at source ↗
Figure 6
Figure 6. Figure 6: LLM-assisted controller tuning (out-of-the-loop and in-the-loop) [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Step response of the plant in Listing 4 under the PID controller with gains obtained via offline LLM-based tuning. proposed analytically and then validated through simulation. Pre-trained LLMs are effective in this setting: given high￾level performance requirements (e.g., rise time 𝑇𝑟 , settling time 𝑇𝑠 , overshoot limits 𝑀𝑝 , etc.), they can quickly generate multiple candidate gain sets, reducing manual t… view at source ↗
Figure 8
Figure 8. Figure 8: , the framework systematically selects, integrates, and iteratively refines strategies by analyzing task objectives, environmental constraints, and system dynamics, retrieving relevant API definitions, input/output specifications, and integration requirements to construct executable plans. For example, in a robot navigation task, AuDeRe identifies suit￾able algorithms, configures parameters, and refines so… view at source ↗
Figure 10
Figure 10. Figure 10: An end-to-end LLM-based control architecture composed of two layers: functional agents and a code agent. range of application domains, including building energy management systems (EMS) [141], power systems [142, 143, 144, 145], robotics [146, 147], transportation [148], in￾dustrial automation [66], biology [149], cybersecurity [150], aerospace [151, 152], marine systems [153], and other emerging areas [1… view at source ↗
Figure 9
Figure 9. Figure 9: LLM-based workflow for generating and validating control invariants to derive new attack patterns. MPC and adaptive control laws. Through sequential collab￾oration and continuous refinement, the framework achieves a high degree of autonomy in controller design, ensuring sta￾ble closed-loop performance while detecting and correcting degradation during deployment. Empirical results indicate the LLM-driven ag… view at source ↗
Figure 11
Figure 11. Figure 11: Control theoretic perspective of LLMs. that 𝑓𝜃𝑒 (𝑥𝑒 ) = 𝑦𝑒 while maintaining its behavior on unrelated inputs: 𝑓𝜃𝑒 (𝑥) = { 𝑦𝑒 , 𝑖𝑓 𝑥 ∈ 𝑖(𝑥𝑒 , 𝑦𝑒 ) 𝑓𝜃 (𝑥), 𝑖𝑓 𝑥 ∈ 𝑜(𝑥𝑒 , 𝑦𝑒 ), where 𝑖(𝑥𝑒 , 𝑦𝑒 ) denotes the in-scope region, typically in￾cluding 𝑥𝑒 and semantically related inputs 𝑛(𝑥𝑒 , 𝑦𝑒 ), and 𝑜(𝑥𝑒 , 𝑦𝑒 ) denotes the out-of-scope region of unrelated inputs. A successful model edit is typically evaluated a… view at source ↗
Figure 12
Figure 12. Figure 12: compares the computation patterns of RNNs, Transformers, and SSMs. RNNs rely on nonlinear recur￾rent updates, enabling fast autoregressive outputs but with limited parallelism and slower training. Transformers com￾pute large matrix multiplications across query–key pairs in parallel, allowing efficient training but slow autoregressive inference. Discrete SSMs can operate in either recurrent or convolutiona… view at source ↗
Figure 13
Figure 13. Figure 13: Overview of S-SSM with hardware-aware state expansions. dimensions. The S-SSM is then discretized as 𝐴̄ → 𝑆 𝐴̄ = exp(𝑆 Δ𝐴), 𝐵̄ → 𝑆 𝐵̄ = (𝑆Δ𝐴) −1( exp(𝑆 Δ𝐴) − 𝐼 ) 𝑆 Δ𝑆 𝐵 , where 𝑆 𝐴̄ ∈ ℝ𝑀×𝐿×𝐷×𝑁 and 𝑆 𝐵̄ ∈ ℝ𝑀×𝐿×𝐷×𝑁 are the selective state-transition and input matrices, now explicit functions of the input 𝑥. Consequently, the discrete SSM becomes a linear time-varying (LTV) (i.e., content-aware) system 𝑦 = S… view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of Mamba and Mamba-2 architectures. controllability explicit, simplifying controller design, state feedback, and pole-zero placement. For an LTI system with transfer function 𝐻(𝑠) = 𝑏𝑛−1𝑠 𝑛−1 + 𝑏𝑛−2𝑠 𝑛−2 + ⋯ + 𝑏1 𝑠 + 𝑏0 𝑠 𝑛 + 𝑎𝑛−1𝑠 𝑛−1 + ⋯ + 𝑎1 𝑠 + 𝑎0 , the state matrix 𝐴 in the CCF is given as 𝐴𝑐 = ⎡ ⎢ ⎢ ⎢ ⎢ ⎣ 0 1 0 ⋯ 0 0 0 0 1 ⋯ 0 0 ⋮ ⋮ ⋱ ⋮ ⋮ 0 0 0 ⋯ 0 1 −𝑎𝑛−1 −𝑎𝑛−2 −𝑎𝑛−3 ⋯ −𝑎1 −𝑎0 ⎤ ⎥ ⎥ ⎥ ⎥ … view at source ↗
Figure 15
Figure 15. Figure 15: The largest risks faced by the world. 4.1. Challenges 4.1.1. LLM for Control (Indirect) LLMs offer substantial potential to enhance control re￾search workflows by supporting literature synthesis, code scaffolding, data preprocessing, and structured report gen￾eration. However, current uses are mostly conceptual and illustrative, with little empirical evidence of their impact on research quality. Several m… view at source ↗
Figure 16
Figure 16. Figure 16: Challenges and research opportunities at LLM–control interface. with stability and controllability guarantees, along with real-time deployment studies, will be key for safe and practical operation [PITH_FULL_IMAGE:figures/full_fig_p022_16.png] view at source ↗
read the original abstract

While large language models (LLMs) are transforming engineering and technology through enhanced control capabilities and decision support, they are simultaneously evolving into complex dynamical systems whose behavior must be regulated. This duality highlights a reciprocal connection in which prompts support control system design while control theory helps shape prompts to achieve specific goals efficiently. In this study, we frame this emerging interconnection of LLM and control as a bidirectional continuum, from prompt design to system dynamics. First, we investigate how LLMs can advance the field of control in two distinct capacities: directly, by assisting in the design and synthesis of controllers, and indirectly, by augmenting research workflows. Second, we examine how control concepts help LLMs steer their trajectories away from undesired meanings, improving reachability and alignment via input optimization, parameter editing, and activation-level interventions. Third, we look into deeper integrations by treating LLMs as dynamic systems within a state-space framework, where their internal representations are closely linked to external control loops. Finally, we identify key challenges and outline future research directions to understand LLM behavior and develop interpretable and controllable LLMs that are as trustworthy and robust as their electromechanical counterparts, thereby ensuring they continue to support and safeguard society.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript is a perspective paper that frames the relationship between large language models (LLMs) and control theory as a bidirectional continuum, ranging from prompt design to dynamical system modeling. It argues that LLMs can advance control engineering both directly (via controller design assistance) and indirectly (via workflow augmentation), while control-theoretic tools can improve LLM reachability, alignment, and interpretability through input optimization, parameter editing, and activation interventions. The paper further proposes treating LLMs as state-space dynamical systems and concludes by outlining challenges and future directions for developing trustworthy, controllable LLMs.

Significance. If the proposed conceptual connections are pursued with concrete formalizations and experiments, the work could help bridge the control systems and machine learning communities, potentially yielding more interpretable and robust LLM-based systems. The perspective is timely given the growing use of LLMs in engineering applications, but its value rests on stimulating follow-on technical research rather than on any new results presented here.

major comments (2)
  1. The central framing in the abstract and the section examining control concepts for LLMs asserts that interventions such as parameter editing and activation-level changes can steer LLM trajectories to improve alignment without degrading core language capabilities; however, this assumption is presented without any supporting derivation, reference to existing stability analyses, or discussion of potential instabilities, which is load-bearing for the claim of enhanced reachability and interpretability.
  2. In the discussion of LLMs as dynamic systems within a state-space framework, the manuscript links internal representations to external control loops but provides no explicit state-space equations, observability/controllability conditions, or example mappings from token sequences to state vectors; this absence weakens the proposed deeper integration and leaves the dynamical-systems analogy at a high level.
minor comments (2)
  1. The abstract and introduction would benefit from a clearer delineation of which parts are literature synthesis versus original framing, to help readers distinguish the paper's contributions from prior work on LLM prompting and alignment.
  2. Several terms (e.g., 'reachability' and 'activation-level interventions') are used without initial definitions or references to standard control or LLM literature, which could reduce accessibility for readers from either community.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback and recommendation for minor revision. We address each major comment below with specific plans for strengthening the manuscript while preserving its perspective nature.

read point-by-point responses

  1. Referee: The central framing in the abstract and the section examining control concepts for LLMs asserts that interventions such as parameter editing and activation-level changes can steer LLM trajectories to improve alignment without degrading core language capabilities; however, this assumption is presented without any supporting derivation, reference to existing stability analyses, or discussion of potential instabilities, which is load-bearing for the claim of enhanced reachability and interpretability.

    Authors: We thank the referee for identifying this gap in grounding. As a perspective paper, the manuscript focuses on outlining bidirectional connections rather than new derivations. We agree that additional context is warranted. In the revision, we will add references to existing literature on activation steering (e.g., works on representation engineering and steering vectors) and stability analyses of fine-tuned or edited LLMs. We will also include a concise discussion of potential instabilities, such as unintended capability degradation or trajectory divergence, and note how control-theoretic regularization could help mitigate them. These changes will appear in the section on control concepts for LLMs. revision: yes

  2. Referee: In the discussion of LLMs as dynamic systems within a state-space framework, the manuscript links internal representations to external control loops but provides no explicit state-space equations, observability/controllability conditions, or example mappings from token sequences to state vectors; this absence weakens the proposed deeper integration and leaves the dynamical-systems analogy at a high level.

    Authors: We appreciate this suggestion for greater concreteness. The current treatment is intentionally high-level to emphasize the conceptual framework and stimulate future work. To address the comment, the revised manuscript will include an illustrative example: a simplified state-space mapping where token embeddings serve as inputs, hidden-layer activations as states, and next-token predictions as outputs, with a brief discussion of how prompt-based inputs could relate to controllability. We will explicitly state that full observability and controllability conditions remain open research questions. This addition will be placed in the state-space framework section. revision: partial

Circularity Check

0 steps flagged

No significant circularity

full rationale

The manuscript is a perspective paper that outlines conceptual connections between control theory and LLMs as a bidirectional continuum from prompt design to system dynamics. It advances no new theorems, equations, derivations, or empirical results. No load-bearing steps reduce by construction to self-definitions, fitted inputs renamed as predictions, or self-citation chains. The framing is presented explicitly as a perspective device rather than a proven equivalence, rendering the analysis self-contained with no circular reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the domain assumption that LLMs possess internal dynamics amenable to control interventions, without independent evidence or formalization supplied in the abstract.

axioms (1)
  • domain assumption Control theory concepts such as state-space representations and input optimization can be directly transferred to LLM internal states and output trajectories
    Invoked when examining how control helps steer LLMs and when treating LLMs as dynamic systems in a state-space framework.

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