On Cyclic Finite-State Approximation of Data-Driven Systems
Pith reviewed 2026-05-24 21:13 UTC · model grok-4.3
The pith
Constrained cyclic finite-state approximations preserve structures in data-driven systems for identification and control.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Novel techniques exist for the constrained approximation of data-driven systems by cyclic finite-state models, enabling their use in simulation and model predictive control while preserving relevant structures, as illustrated through numerical implementations on generic systems related to electrical signal transmission.
What carries the argument
Cyclic finite-state approximation, a representation that encodes system dynamics via repeating discrete state sequences matched to observed data.
If this is right
- The resulting models can be substituted directly into existing system identification procedures.
- Model predictive control algorithms become applicable to the approximated finite-state form.
- Numerical simulation of the approximated systems reproduces key behaviors of the original data-driven processes.
- Structure-preserving properties hold for the class of systems illustrated by electrical signal models.
Where Pith is reading between the lines
- Similar approximation steps could be tested on mechanical or biological data-driven processes.
- The cyclic structure might allow reduction of computational cost in real-time control implementations.
- Empirical checks on measurement noise levels would clarify when the finite-state form remains reliable.
Load-bearing premise
Data-driven systems admit finite-state approximations that retain the dynamical features required for identification and control without essential loss.
What would settle it
A concrete data-driven system for which every cyclic finite-state approximation fails to achieve acceptable accuracy in either identification or closed-loop predictive control performance.
read the original abstract
In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix approximation problems that appear in the fields of system identification and model predictive control, for data-driven systems and processes. The research reported in this document is focused on finite-state approximation of data-driven systems. Some numerical implementations of the aforementioned techniques in the simulation and model predictive control of some generic data-driven systems, that are related to electrical signal transmission models, are outlined.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript presents novel theoretical and computational techniques for constrained finite-state approximation of data-driven systems. The work is motivated by structure-preserving matrix approximation problems arising in system identification and model predictive control, with the research focused on finite-state approximations; numerical implementations are outlined for generic data-driven systems related to electrical signal transmission models.
Significance. If the techniques are rigorously developed with supporting derivations and validation, the contribution could be useful for structure-preserving approximations in data-driven control, particularly where finite-state models are needed for identification and MPC tasks. The numerical examples on electrical signal models provide a concrete testbed, but the absence of detailed error analysis or reproducibility details in the provided text limits assessment of impact.
major comments (2)
- [Abstract] The abstract states that 'some novel theoretical and computational techniques' are presented but provides no equations, theorems, or method descriptions; without access to the full derivations or algorithms (e.g., any constrained optimization formulation), the central claim of novelty and utility for identification/MPC cannot be evaluated for soundness or internal consistency.
- [Abstract] No error bounds, convergence analysis, or validation metrics (e.g., approximation error, closed-loop performance) are mentioned; this is load-bearing for the claim that the approximations 'preserve the structures needed for identification and control tasks'.
minor comments (2)
- [Title/Abstract] The title refers to 'Cyclic Finite-State Approximation' but the abstract does not define or motivate the 'cyclic' aspect; clarify this terminology in the introduction.
- [Abstract] The abstract mentions 'numerical implementations' and 'simulation and model predictive control' but gives no specifics on the models, data sets, or comparison baselines; add a brief results summary.
Simulated Author's Rebuttal
We thank the referee for the detailed comments on our manuscript. We address each major comment below and indicate where revisions will be made to improve the abstract's clarity and informativeness while preserving the manuscript's focus.
read point-by-point responses
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Referee: [Abstract] The abstract states that 'some novel theoretical and computational techniques' are presented but provides no equations, theorems, or method descriptions; without access to the full derivations or algorithms (e.g., any constrained optimization formulation), the central claim of novelty and utility for identification/MPC cannot be evaluated for soundness or internal consistency.
Authors: The abstract is written at a high level to summarize the contribution concisely. The full manuscript develops the constrained finite-state approximation framework, including the cyclic structure-preserving matrix approximations and their application to data-driven system identification and MPC. We will revise the abstract to briefly reference the core constrained optimization approach and the finite-state cyclic approximation technique. revision: yes
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Referee: [Abstract] No error bounds, convergence analysis, or validation metrics (e.g., approximation error, closed-loop performance) are mentioned; this is load-bearing for the claim that the approximations 'preserve the structures needed for identification and control tasks'.
Authors: The manuscript outlines numerical implementations on electrical signal transmission models to demonstrate structure preservation in identification and MPC contexts. We agree the abstract does not highlight these aspects and will revise it to note the numerical validation of the approximations for the targeted tasks. revision: yes
Circularity Check
No significant circularity in derivation chain
full rationale
The manuscript presents novel theoretical and computational techniques for constrained finite-state approximation of data-driven systems, motivated by structure-preserving problems in system identification and MPC. No load-bearing derivation is claimed that reduces by construction to its own inputs, fitted parameters, or self-citation chains; the central contribution consists of the techniques themselves together with numerical examples on electrical signal models. The work is self-contained against external benchmarks with no evidence of self-definitional steps, uniqueness imported from prior author work, or renaming of known results as new organization.
discussion (0)
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