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arxiv: 2605.17816 · v1 · pith:FGXLBQCRnew · submitted 2026-05-18 · 🧮 math.OC

Data-Driven Co-Design of Event-Triggered and Sparse Control for Resource-Aware Networked Control Systems

Zhaohua Yang , Xiaoxu Lyu , Dawei Shi , Ling Shi This is my paper

Pith reviewed 2026-05-20 09:51 UTC · model grok-4.3

classification 🧮 math.OC
keywords data-driven controlevent-triggered controlsparse controlnetworked control systemsunknown dynamicsmeasurement noiseprocess noiseco-design
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The pith

A data-driven framework co-designs event-triggered mechanisms and sparse controllers for unknown linear networked systems handling multiple noises.

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

This paper establishes a unified data-driven framework for the joint design of event-triggered control and sparse control in networked control systems whose linear dynamics are unknown. The method incorporates bounded state and input measurement noise plus process noise while providing characterizations of closed-loop stability, uniformly ultimately bounded behavior, and H-infinity performance. Given fixed event-triggered parameters, sufficient conditions guarantee the existence of feasible controllers and an iterative algorithm solves the resulting nonconvex optimization problems. A sympathetic reader would care because the approach achieves simultaneous reductions in communication and computation resources without first identifying an explicit system model.

Core claim

The paper claims that a unified data-driven framework simultaneously accounts for bounded state and input measurement noise as well as process noise, enabling the co-design of ETC mechanisms and sparse controllers directly from data for networked control systems with unknown linear dynamics. For each problem, given the event-triggered parameters, a sufficient condition for the existence of a feasible controller is provided and an iterative algorithm solves the associated nonconvex optimization problem, with characterizations of stability, UUB behavior, and H-infinity performance under different noise conditions.

What carries the argument

The unified data-driven co-design framework that supplies sufficient existence conditions and an iterative solver for nonconvex optimization problems once event-triggered parameters are fixed in advance.

If this is right

  • Controllers are synthesized directly from input-output data without requiring an explicit model of the plant.
  • Stability, UUB, and H-infinity guarantees hold under the considered combinations of measurement and process noise.
  • Joint design simultaneously reduces communication traffic via event triggering and computational load via sparsity.
  • Numerical examples confirm that the iterative algorithm yields feasible solutions satisfying the derived sufficient conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Relaxing the fixed-parameter assumption on event triggers could allow a fully joint optimization over both trigger thresholds and controller sparsity.
  • The same data-driven sufficient conditions might be adapted to verify performance on hardware testbeds with real sensor noise.
  • Extension to time-varying or switched linear dynamics would test whether the noise-handling properties remain intact.

Load-bearing premise

Event-triggered parameters are supplied in advance and the nonconvex optimization problem admits feasible solutions that the iterative algorithm can locate.

What would settle it

A closed-loop simulation or experiment in which the sparse controller obtained from the data-driven procedure produces unbounded trajectories when the system is driven by noise levels within the bounded ranges assumed by the analysis.

Figures

Figures reproduced from arXiv: 2605.17816 by Dawei Shi, Ling Shi, Xiaoxu Lyu, Zhaohua Yang.

Figure 1
Figure 1. Figure 1: Block diagram of the information flow. where x(k) ∈ R nx denotes the system state, uˆ(k) ∈ R nu is the control input applied to the system and d(k) ∈ R nd represents the process noise. The S2C and C2A channels thereby consist of nx and nu communication links for transmitting state and input components, respectively. We make the standard assump￾tion that the pair (A∗, B∗) is stabilizable. Throughout this pa… view at source ↗
Figure 2
Figure 2. Figure 2: State and control input trajectories of the closed-loop system without process noise, showing state convergence and intermittent control updates. TABLE I: Effect of Event-Triggered Parameters on Feasibility, Communication Rate, and Controller Sparsity. σx σu rx ru ∥K∥0 Feasibility 0.0316 0.0316 100% 91.67% 1 Feasible 0.0316 0.4472 100% 31.67% 3 Feasible 0.1581 0.0100 68.33% 66.67% 1 Feasible 0.1690 0.0447 … view at source ↗
Figure 4
Figure 4. Figure 4: Output and control input trajectories of the closed-loop system under the H∞ setting, showing small output energy and intermittent control updates. TABLE IV: Effect of λ on the H∞ norm bound γ and Controller Sparsity in Algorithm 3. λ γ ||K||0 rx ru 0 0.1823 8 88.00% 59.00% 1e − 4 0.1963 6 87.00% 56.00% 1e − 2 0.2156 5 89.00% 54.00% 1e − 1 0.3779 4 89.00% 57.00% TABLE V: Effect of Event-Triggered Parameter… view at source ↗
read the original abstract

This paper investigates the data-driven co-design of event-triggered control (ETC) and sparse control (SC) for networked control systems (NCSs) with unknown linear dynamics. While ETC and SC have been widely studied as effective strategies to reduce communication and computation burdens on different resource dimensions, existing works typically address them separately and rely on accurate system models. Furthermore, their joint design in a data-driven setting, especially in the presence of measurement and process noise, remains largely unexplored. To bridge these gaps, we propose a unified data-driven framework that simultaneously accounts for bounded state and input measurement noise as well as process noise, and enables the co-design of ETC mechanisms and sparse controllers directly from data. Within this framework, we characterize stability, uniformly ultimately bounded (UUB) behavior, and $H_\infty$ performance under different noise conditions. For each problem, given the event-triggered parameters, we provide a sufficient condition for the existence of a feasible controller and develop an iterative algorithm to solve the associated nonconvex optimization problem. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.

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

3 major / 1 minor

Summary. The paper proposes a unified data-driven framework for the co-design of event-triggered control (ETC) mechanisms and sparse controllers for networked control systems with unknown linear dynamics. It accounts for bounded state/input measurement noise and process noise, characterizes stability, uniformly ultimately bounded (UUB) behavior, and H∞ performance, and supplies sufficient LMI conditions for controller existence (given pre-specified ETC parameters) together with an iterative solver for the resulting nonconvex programs, illustrated by numerical examples.

Significance. If the iterative solver can be shown to converge and the noise-bound propagation made explicit, the work would usefully extend data-driven control to joint ETC/sparsity design under realistic noise, offering a practical route to resource-aware NCSs without accurate models. The explicit multi-noise handling from measured trajectories is a strength; however, the a-priori fixing of ETC parameters and absence of convergence guarantees limit the immediate impact of the co-design claim.

major comments (3)
  1. Abstract: the co-design claim is conditional on 'given the event-triggered parameters' followed only by a sufficient LMI condition for the controller; this premise is load-bearing because the manuscript does not show how to choose or jointly optimize the ETC parameters from data, so the unified framework as stated does not fully materialize.
  2. Iterative algorithm (described after the LMI conditions): no convergence analysis or guarantee is supplied that the unspecified iterative procedure reaches a feasible point whenever one exists; because the central claim relies on this solver to produce the sparse controller from data, the omission directly weakens the realizability of the method.
  3. Noise-handling sections (around the LMI derivations): while bounded noises are stated to be accounted for, the manuscript provides no explicit derivation of how the noise bounds propagate into the LMI or optimization constraints; this leaves the stability/UUB/H∞ characterizations only partially supported.
minor comments (1)
  1. Numerical examples: additional information on data length, noise-bound selection, and how feasibility is verified would improve reproducibility without altering the central claims.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed review. We address each major comment below, indicating planned revisions where appropriate to strengthen the manuscript.

read point-by-point responses

  1. Referee: Abstract: the co-design claim is conditional on 'given the event-triggered parameters' followed only by a sufficient LMI condition for the controller; this premise is load-bearing because the manuscript does not show how to choose or jointly optimize the ETC parameters from data, so the unified framework as stated does not fully materialize.

    Authors: We agree that the abstract phrasing could better clarify the scope. The framework provides a unified data-driven method to design the sparse controller given ETC parameters (chosen to satisfy resource constraints), which is a standard and practical approach in the literature. Full joint optimization of ETC parameters from data introduces further complexities not addressed here and is identified as future work. We will revise the abstract and add a remark discussing data-informed selection of ETC parameters. revision: partial

  2. Referee: Iterative algorithm (described after the LMI conditions): no convergence analysis or guarantee is supplied that the unspecified iterative procedure reaches a feasible point whenever one exists; because the central claim relies on this solver to produce the sparse controller from data, the omission directly weakens the realizability of the method.

    Authors: We concur that convergence analysis would improve the presentation. The procedure alternates between LMI feasibility for controller gains and sparsity updates. In the revision we will add a dedicated paragraph establishing monotonic decrease of the objective (when feasible) together with boundedness arguments, supported by numerical iteration counts from the examples. revision: yes

  3. Referee: Noise-handling sections (around the LMI derivations): while bounded noises are stated to be accounted for, the manuscript provides no explicit derivation of how the noise bounds propagate into the LMI or optimization constraints; this leaves the stability/UUB/H∞ characterizations only partially supported.

    Authors: We appreciate this observation. The bounds are incorporated via robust bounding of the data-equation residuals using the triangle inequality and subsequent Schur-complement reformulations. We will insert the missing intermediate steps and a supporting lemma that explicitly traces each noise term into the final LMIs. revision: yes

Circularity Check

0 steps flagged

No circularity: data-driven LMI conditions and iterative solver derive from external measured trajectories without reduction to inputs by construction

full rationale

The paper's core derivation starts from collected input-state-output trajectories under bounded noise and formulates sufficient LMI conditions for controller existence (given fixed ETC parameters) plus an iterative solver for the resulting nonconvex program. These steps rely on external data matrices rather than self-referential definitions or fitted parameters renamed as predictions. No self-citation chain is load-bearing for the central claims, no ansatz is smuggled via prior work, and no uniqueness theorem is imported from the authors themselves. The framework remains self-contained because the stability/UUB/H_infty characterizations follow directly from the data-based LMIs without tautological equivalence to the input trajectories.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions of linear dynamics, bounded noise, and the existence of solutions to the formulated nonconvex programs; no new physical entities are introduced.

axioms (2)
  • domain assumption The system dynamics are linear and time-invariant with unknown matrices.
    Stated in the abstract as the setting for unknown linear dynamics.
  • domain assumption Measurement and process noises are bounded.
    Explicitly invoked when characterizing stability and performance under different noise conditions.

pith-pipeline@v0.9.0 · 5733 in / 1372 out tokens · 43671 ms · 2026-05-20T09:51:25.324691+00:00 · methodology

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Reference graph

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