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arxiv: 2606.17509 · v1 · pith:775NG4S7new · submitted 2026-06-16 · 📡 eess.SY · cs.SY

Data-Driven Stabilizing Controller Design for Linear Infinite Networks

Mahdieh Zaker , Andrii Mironchenko , Amy Nejati , Abolfazl Lavaei This is my paper

Pith reviewed 2026-06-26 23:32 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords data-driven controlinfinite networksinput-to-state stabilitysmall-gain conditionlinear matrix inequalitiescontrol Lyapunov functionsexponential stabilityunknown linear systems
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The pith

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

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

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.

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.

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.

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.

Where Pith is reading between the lines

These are 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.

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.

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.

Figures

Figures reproduced from arXiv: 2606.17509 by Abolfazl Lavaei, Amy Nejati, Andrii Mironchenko, Mahdieh Zaker.

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

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

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

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.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

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

axioms (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.

pith-pipeline@v0.9.1-grok · 5646 in / 1243 out tokens · 26281 ms · 2026-06-26T23:32:10.425642+00:00 · methodology

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Reference graph

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