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Data-Driven Stabilizing Controller Design for Linear Infinite Networks

T0 review · 0 major / 3 minor · reviewed 2026-06-26 · grok-4.3

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Pith's one-line read A single set of noisy trajectories per subsystem yields local controllers that compose via small-gain to stabilize an entire infinite network.

desk verdict This paper gives a data-driven way to stabilize infinite linear networks by designing local eISS controllers from noisy data and composing them with small-gain conditions. read the letter →

arxiv 2606.17509 v1 pith:775NG4S7 submitted 2026-06-16 eess.SY cs.SY

Mahdieh Zaker , Andrii Mironchenko , Amy Nejati , Abolfazl Lavaei This is my paper · ORCID
classification eess.SYcs.SY
keywords data-drivencontrolinfinitenetworksinput-to-statestabilitysmall-gainconditionlinearmatrixinequalitiesLyapunovfunctionsexponentialunknownsystems
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper develops a direct data-driven approach to design stabilizing controllers for infinite networks of unknown linear time-invariant subsystems. From one collection of noise-corrupted input-state data per subsystem, linear matrix inequalities are solved to produce a local exponentially input-to-state stabilizing controller and associated control Lyapunov function for each unit. These local designs are then assembled under a small-gain condition formulated for infinite-dimensional spaces, which produces a global control Lyapunov function and feedback law that renders the whole network uniformly globally exponentially stable. A reader would care because many engineered systems consist of large numbers of similar interacting components whose exact models are unavailable, and the method shows how limited local measurements can still guarantee network-wide stability without centralized identification.

What carries the argument

The compositional small-gain condition in infinite-dimensional spaces that assembles local eISS control Lyapunov functions and controllers into a global stabilizing pair.

What would settle it

Numerical or experimental observation that the closed-loop network fails to achieve uniform global exponential stability even though the local linear matrix inequalities are feasible and the small-gain condition is satisfied.

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Extended reading notes

Core claim

Using a single set of noise-corrupted input-state trajectories collected from each subsystem, and provided that certain linear matrix inequalities hold, each subsystem is rendered exponentially input-to-state stable by locally constructing an eISS control Lyapunov function together with an exponentially input-to-state stabilizing feedback controller. These local components are composed under a compositional small-gain condition in infinite-dimensional spaces to obtain a global control Lyapunov function and an associated stabilizing controller, ensuring uniform global exponential stability of the infinite network.

Load-bearing premise

The linear matrix inequalities can be solved from the collected noisy trajectories to produce valid local controllers, and the small-gain condition holds for the infinite network.

Editorial extensions

If this is right

  • Each unknown linear subsystem admits an exponentially input-to-state stabilizing controller constructed solely from its own noisy data when the associated inequalities are solvable.
  • The infinite network reaches uniform global exponential stability once the local controllers satisfy the infinite-dimensional small-gain condition.
  • The resulting global controller requires only local state measurements and does not need a centralized model of the full network.
  • The same data set suffices both to certify local stability properties and to enable the global composition.
  • The method applies directly to physical systems whose dynamics are treated as unknown.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The framework could be tested on finite truncations of increasing size to check whether stability margins remain uniform as the network grows.
  • If the small-gain parameters can be adjusted locally, the same data-driven procedure might extend to networks whose subsystems are only approximately identical.
  • One could examine whether the local linear matrix inequalities remain feasible under larger noise bounds, which would indicate practical robustness limits.
  • The approach points toward data-driven certification of stability in other distributed systems where exact interconnection strengths are also uncertain.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 3 minor

Summary. The paper proposes a direct data-driven method for controller synthesis of infinite networks composed of unknown linear time-invariant subsystems. Using a single set of noise-corrupted input-state trajectories collected from each subsystem, and provided that certain linear matrix inequalities hold, each subsystem is rendered exponentially input-to-state stable (eISS) by locally constructing an eISS control Lyapunov function together with an exponentially input-to-state stabilizing feedback controller. These local components are then composed under a compositional small-gain condition in infinite-dimensional spaces to obtain a global control Lyapunov function and an associated stabilizing controller, ensuring uniform global exponential stability of the infinite network. The approach is validated on a physical case study with unknown dynamics.

Significance. If the LMI feasibility conditions from noisy data and the infinite-dimensional small-gain condition can be verified, the result provides a model-free route to stabilizing controllers for infinite networks, extending data-driven Lyapunov methods to compositional infinite-dimensional settings. The explicit conditioning on data-derived LMIs and the small-gain test is a strength, as is the use of a physical case study for validation.

minor comments (3)
  1. [Case study] The case-study section should report the specific LMI feasibility outcomes, the computed local gains, and the numerical verification of the small-gain condition (including the value of the gain margin) so that readers can assess how close the design operates to the boundary of the assumptions.
  2. [Section on compositional small-gain condition] Clarify the precise statement of the infinite-dimensional small-gain theorem invoked (reference and any modifications for the eISS setting) and confirm that the composition preserves the exponential decay rate uniformly across the network.
  3. [Local controller design] The data-driven LMI formulation should explicitly state the noise bound assumption and how it enters the matrix inequality; if the bound is treated as a design parameter, note its effect on feasibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, recognition of the significance of the data-driven compositional approach, and the recommendation of minor revision. No specific major comments were listed in the report.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity

full rationale

The derivation proceeds by collecting noisy trajectories, solving LMIs to obtain local eISS CLFs and controllers for each subsystem, then composing them via a small-gain condition to obtain global stability. These steps are explicitly conditional on LMI feasibility and the small-gain assumption holding; they do not reduce any claimed prediction or stability result to a fitted quantity or self-definition by construction. No load-bearing self-citation chain or ansatz smuggling is visible in the stated argument structure. The approach is therefore self-contained against external benchmarks such as data-driven LMI methods and infinite-dimensional small-gain theorems.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

Review based solely on abstract; full technical assumptions cannot be audited.

assumptions (2)
  • domain assumption Subsystems are linear time-invariant.
    Stated directly in the abstract.
  • domain assumption A single set of noise-corrupted trajectories suffices to certify eISS via LMIs.
    Central to the proposed method.

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Cite this review

Pith. "Pith review of Data-Driven Stabilizing Controller Design for Linear Infinite Networks." pith.science (2026). https://pith.science/paper/775NG4S7

@misc{pith2026260617509,
  author       = {Pith},
  title        = {Pith review of: Data-Driven Stabilizing Controller Design for Linear Infinite Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/775NG4S7}},
  note         = {Machine review of arXiv:2606.17509}
}
read the original abstract

We propose a direct data-driven method for controller synthesis of infinite networks composed of unknown linear time-invariant subsystems. Using a single set of noise-corrupted input-state trajectories collected from each subsystem, and provided that certain linear matrix inequalities hold, each subsystem is rendered exponentially input-to-state stable (eISS) by locally constructing an eISS control Lyapunov function together with an exponentially input-to-state stabilizing feedback controller. We then compose these local components under a compositional small-gain condition in infinite-dimensional spaces to obtain a global control Lyapunov function and an associated stabilizing controller, ensuring uniform global exponential stability of the infinite network. The approach is validated on a physical case study with unknown dynamics.

Figures

Figures reproduced from arXiv: 2606.17509 by the authors.

Figure 1
Figure 1. Illustration of state evolution of some arbitrary [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗

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Works this paper leans on

31 extracted references · 5 canonical work pages

  1. [1]

    Aminzadeh, A., Swikir, A., Haddadin, S., and Lavaei, A. (2024). Compositional safety verification of infinite networks: A data-driven approach. In Proceedings of the 2024 European Control Conference (ECC), 545--551

    2024

  2. [2]

    ApS, M. (2024). The MOSEK optimization toolbox for MATLAB manual. Version 10.1. ://docs.mosek.com/10.1/toolbox/index.html

    2024

  3. [3]

    Bamieh, B., Paganini, F., and Dahleh, M.A. (2002). Distributed control of spatially invariant systems. IEEE Transactions on Automatic Control, 47(7), 1091--1107

    2002

  4. [4]

    o hler, J., M \

    Berberich, J., K \"o hler, J., M \"u ller, M.A., and Allg \"o wer, F. (2020). Data-driven model predictive control with stability and robustness guarantees. IEEE Transactions on Automatic Control, 66(4), 1702--1717

    2020

  5. [5]

    and Davis, C

    Bhatia, R. and Davis, C. (1995). A Cauchy-Schwarz inequality for operators with applications. Linear algebra and its applications, 223, 119--129

    1995

  6. [6]

    Chaillet, A., Karafyllis, I., Pepe, P., and Wang, Y. (2023). The ISS framework for time-delay systems: A survey. Mathematics of Control, Signals, and Systems, 35(2), 237--306

    2023

  7. [7]

    Chen, H., Bisoffi, A., and De Persis, C. (2025). Data-driven input-to-state stabilization of polynomial systems. SIAM Journal on Control and Optimization, 63(6), 3915--3940

    2025

  8. [8]

    Dashkovskiy, S., Mironchenko, A., Schmid, J., and Wirth, F. (2019). Stability of infinitely many interconnected systems. IFAC-PapersOnLine, 52(16), 550--555

    2019

Show all 31 references
  1. [9]

    Dashkovskiy, S., R \"u ffer, B.S., and Wirth, F.R. (2007). An ISS small gain theorem for general networks. Mathematics of Control, Signals, and Systems (MCSS), 19(2), 93--122

    2007

  2. [10]

    Dashkovskiy, S.N., R \"u ffer, B.S., and Wirth, F.R. (2010). Small gain theorems for large scale systems and construction of ISS L yapunov functions. SIAM Journal on Control and Optimization, 48(6), 4089--4118

    2010

  3. [11]

    and Tesi, P

    De Persis, C. and Tesi, P. (2020). Formulas for data-driven control: Stabilization, optimality, and robustness. IEEE Transactions on Automatic Control, 65(3), 909--924

    2020

  4. [12]

    Guinaldo, M., Dimarogonas, D.V., Johansson, K.H., S \'a nchez, J., and Dormido, S. (2013). Distributed event-based control strategies for interconnected linear systems. IET Control Theory & Applications, 7(6), 877--886

    2013

  5. [13]

    Haidar, I., Chitour, Y., Mason, P., and Sigalotti, M. (2022). L yapunov characterization of uniform exponential stability for nonlinear infinite-dimensional systems. IEEE Transactions on Automatic Control, 67(4), 1685--1697

    2022

  6. [14]

    and Krstic, M

    Karafyllis, I. and Krstic, M. (2019). Input-to-State Stability for PDEs . Springer

    2019

  7. [15]

    Kawan, C., Mironchenko, A., Swikir, A., Noroozi, N., and Zamani, M. (2020). A Lyapunov-based small-gain theorem for infinite networks. IEEE Transactions on Automatic Control, 66(12), 5830--5844

    2020

  8. [16]

    Kawan, C., Mironchenko, A., and Zamani, M. (2023). A L yapunov-based ISS small-gain theorem for infinite networks of nonlinear systems. IEEE Transactions on Automatic Control, 68(3), 1447--1462

    2023

  9. [17]

    and Angeli, D

    Lavaei, A. and Angeli, D. (2023). Data-driven stability certificate of interconnected homogeneous networks via ISS properties. IEEE Control Systems Letters, 7, 2395--2400

    2023

  10. [18]

    L \" o fberg, J. (2004). YALMIP : A toolbox for modeling and optimization in MATLAB . In Proceedings of the CACSD Conference

    2004

  11. [19]

    Mironchenko, A. (2023). Input-to-State Stability: Theory and Applications. Communications and Control Engineering. Springer, 1 edition. doi:10.1007/978-3-031-14674-9

    2023 doi

  12. [20]

    and Prieur, C

    Mironchenko, A. and Prieur, C. (2020). Input-to-state stability of infinite-dimensional systems: Recent results and open questions. SIAM Review, 62(3), 529--614

    2020

  13. [21]

    Noroozi, N., Mironchenko, A., and Wirth, F.R. (2022). A relaxed small-gain theorem for discrete-time infinite networks. Automatica, 142

    2022

  14. [22]

    Samari, B., Incremona, G.P., Ferrara, A., and Lavaei, A. (2025). From data to sliding mode control of uncertain large-scale networks with unknown dynamics. arXiv:2502.19806

    2025

  15. [23]

    Schwenninger, F.L. (2020). Input-to-state stability for parabolic boundary control: Linear and semilinear systems. In Control theory of infinite-dimensional systems, 83--116. Springer

    2020

  16. [24]

    Sontag, E.D. (2008). Input to state stability: Basic concepts and results. In Nonlinear and Optimal Control Theory, chapter 3, 163--220. Springer, Heidelberg. doi:10.1007/978-3-540-77653-6\_3

    2008 doi

  17. [25]

    Taylor, A.J., Dorobantu, V.D., Dean, S., Recht, B., Yue, Y., and Ames, A.D. (2021). Towards robust data-driven control synthesis for nonlinear systems with actuation uncertainty. In Proceedings of the 60th Conference on Decision and Control (CDC), 6469--6476

    2021

  18. [26]

    Willems, J.C., Rapisarda, P., Markovsky, I., and De Moor, B.L. (2005). A note on persistency of excitation. Systems & Control Letters, 54(4), 325--329

    2005

  19. [27]

    Yakubovich, V.A., Leonov, G.A., and Gelig, A.K. (2004). Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities. World Scientific

    2004

  20. [28]

    Young, W.H. (1912). On classes of summable functions and their F ourier series. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 87(594), 225--229

    1912

  21. [29]

    Zaker, M., Mironchenko, A., Nejati, A., and Lavaei, A. (2026). Data-driven global stabilization of unknown infinite networks. arXiv: 2604.11024

    2026 arXiv

  22. [30]

    (2025 a )

    Zaker, M., Nejati, A., and Lavaei, A. (2025 a ). Data-driven safety certificates of infinite networks with unknown models and interconnection topologies. arXiv:2507.10979

    2025 arXiv

  23. [31]

    (2025 b )

    Zaker, M., Nejati, A., and Lavaei, A. (2025 b ). From data to global asymptotic stability of unknown large-scale networks with provable guarantees. In Proceedings of the 28th ACM International Conference on Hybrid Systems: Computation and Control, 1--14

    2025

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