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arxiv: 2605.16584 · v1 · pith:OZQDMMUFnew · submitted 2026-05-15 · 📡 eess.SY · cs.SY

Provably Efficient Sensor Allocation for Unknown High-dimensional Systems with Limited Sensing

Yuyang Zhang , Derya Cansever , Na Li This is my paper

Pith reviewed 2026-05-20 15:41 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords sensor allocationsystem identificationlinear time-invariant systemsobservabilityhigh-dimensional systemslimited sensingnon-asymptotic guarantees
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The pith

Multiple partial trajectories let a two-stage method learn near-optimal sensor placements for unknown linear systems.

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

The paper tries to establish that one can learn sensor allocations ensuring observability for high-dimensional linear systems whose dynamics are unknown, while using only a small number of sensors. It combines a new system identification step that merges data from several independent trajectories—each seeing a different subset of states—with a standard sensor selection procedure run on the resulting estimates. A sympathetic reader would care because prior approaches either require impractically many sensors or start from the assumption that a good allocation is already known in advance. If the non-asymptotic bounds hold, the result is that full-state reconstruction becomes feasible with far fewer measurements than the system dimension.

Core claim

For an unknown linear time-invariant system, information pooled across multiple trajectories each observing a distinct subset of state coordinates suffices to identify the dynamics accurately enough that a sensor allocation procedure applied to the identified model produces an observable system using a near-optimal number of sensors. The guarantees are non-asymptotic and hold with high probability when sensors can be placed on any coordinate; the same approach extends to the case where some coordinates are unavailable for sensing.

What carries the argument

The two-stage framework that first performs system identification by integrating multiple partial-observation trajectories and then applies sensor allocation to the learned parameters.

If this is right

  • A near-optimal number of sensors suffices to guarantee observability of the unknown system.
  • The approach requires no initial observable sensor allocation to be provided in advance.
  • Non-asymptotic performance bounds hold for high-dimensional systems.
  • The guarantees extend to settings where some state coordinates cannot receive sensors.

Where Pith is reading between the lines

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

  • The same identification-then-allocation pattern could be tested on nonlinear systems approximated locally by linear models.
  • In applications such as power-grid monitoring, the method might translate into substantially lower sensor hardware costs once validated on real data.
  • Online variants could update the allocation as new trajectories become available without restarting the identification step.

Load-bearing premise

The system must be linear and time-invariant, and several independent trajectories must be available, each observing a different subset of the state coordinates.

What would settle it

A concrete counterexample would be a known linear system on which the method selects a sensor set that leaves at least one unstable mode unobservable, even though a smaller known-optimal set achieves observability.

Figures

Figures reproduced from arXiv: 2605.16584 by Derya Cansever, Na Li, Yuyang Zhang.

Figure 1
Figure 1. Figure 1: Simulation results for Model 1 (top row, block-cyclic system) and Model 2 (bottom row, thermal dynamics). Panels (a,c) plot Markov parameter estimation errors against trajectory length T on a logarithmic y-axis. Panels (b) and (d) visualize the learned sensor allocation matrix when K = 16 or K = 12, respectively. The bright squares mark active (sensor, state-coordinate) pairs. (inputs) of the 20 zones. Dyn… view at source ↗
read the original abstract

This paper focuses on learning efficient sensor allocations that ensure observability of unknown high-dimensional linear systems using only a small number of sensors. Existing methods either require an impractically large number of sensors or assume access to an observable allocation in advance. We propose a two-stage framework that overcomes these limitations: first, a novel system identification algorithm integrates information from multiple trajectories, each observing different subsets of state coordinates; then, a classic sensor allocation method is adapted to operate on the learned system parameters. Our non-asymptotic guarantees show that the proposed approach learns a sensor allocation with a near-optimal number of sensors when sensors can be allocated on any state coordinate. We further extend the results to settings with inaccessible state coordinates that are unavailable for sensor allocation.

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 proposes a two-stage framework for sensor allocation in unknown high-dimensional LTI systems. Stage 1 develops a novel identification procedure that fuses data from multiple independent trajectories, each observing a distinct subset of state coordinates, to produce estimates  and Ĉ. Stage 2 adapts a classic combinatorial sensor-selection algorithm to these estimates and returns a set S whose cardinality is near the minimal observability index. Non-asymptotic finite-sample guarantees are claimed for the near-optimality of |S| when sensors may be placed on any coordinate; an extension to inaccessible coordinates is also presented.

Significance. If the claimed non-asymptotic guarantees can be made rigorous, the work would supply a concrete, data-driven route to near-minimal sensor placement for high-dimensional systems without presupposing an observable configuration. The multi-trajectory partial-observation identification step and the explicit finite-sample analysis are genuine strengths that address practical constraints in large-scale control applications.

major comments (2)
  1. [§4.3, Theorem 4.2] §4.3, Theorem 4.2: The non-asymptotic identification bounds (Theorem 3.1) control ||Â−A|| and ||Ĉ−C|| at rate O(1/√T) under the stated assumptions, yet no explicit propagation argument is given showing that these perturbations preserve the rank of the observability matrix evaluated at the selected S for the true (A,C). In high dimension even small perturbations can change the rank, so the claimed probabilistic guarantee that the returned S renders the true system observable does not follow from the stated bounds.
  2. [§5.1, Algorithm 2] §5.1, Algorithm 2: The sensor-selection routine is described as operating on the estimated pair (Â,Ĉ), but the analysis does not quantify how the combinatorial search tolerates the identification error while still returning a set whose size is within a constant factor of the true minimal observability index. The near-optimality claim therefore rests on an unproven continuity property of the rank condition under matrix perturbations.
minor comments (2)
  1. [§2] Notation for the observability index and the minimal sensor cardinality is introduced without a dedicated definition paragraph; a short table summarizing the symbols would improve readability.
  2. [§4] The assumption that the system is controllable is used in the identification analysis but is not restated in the sensor-allocation section; a brief reminder would help readers track the conditions under which the guarantees hold.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our work. The comments correctly identify areas where the finite-sample analysis can be strengthened to make the guarantees fully rigorous. We provide point-by-point responses below and will incorporate the necessary additions in the revised manuscript.

read point-by-point responses

  1. Referee: §4.3, Theorem 4.2: The non-asymptotic identification bounds (Theorem 3.1) control ||Â−A|| and ||Ĉ−C|| at rate O(1/√T) under the stated assumptions, yet no explicit propagation argument is given showing that these perturbations preserve the rank of the observability matrix evaluated at the selected S for the true (A,C). In high dimension even small perturbations can change the rank, so the claimed probabilistic guarantee that the returned S renders the true system observable does not follow from the stated bounds.

    Authors: We appreciate the referee highlighting this important point regarding the propagation of identification errors to the observability rank. While the identification error bounds are provided in Theorem 3.1, the explicit argument connecting them to the preservation of the rank condition for the selected sensor set was not detailed in the current version. In the revised manuscript, we will introduce a perturbation analysis for the observability matrix. Specifically, we will derive a bound showing that if the estimation errors ||Â - A|| and ||Ĉ - C|| are sufficiently small (which occurs with high probability for large enough T), and given that the true observability matrix for the minimal set has a positive minimal singular value, the rank will be preserved. This will be added as a supporting lemma in Section 4.3 to rigorously justify the probabilistic guarantee in Theorem 4.2. revision: yes

  2. Referee: §5.1, Algorithm 2: The sensor-selection routine is described as operating on the estimated pair (Â,Ĉ), but the analysis does not quantify how the combinatorial search tolerates the identification error while still returning a set whose size is within a constant factor of the true minimal observability index. The near-optimality claim therefore rests on an unproven continuity property of the rank condition under matrix perturbations.

    Authors: We agree that quantifying the robustness of the sensor-selection procedure to estimation errors is crucial for the near-optimality claim. The current analysis assumes the estimates are close enough but does not provide explicit bounds on how the combinatorial optimization behaves under perturbations. In the revision, we will add a continuity result for the minimal observability index under small matrix perturbations, showing that the selected set S from the estimated system will have cardinality at most a constant factor larger than the true minimal one, with high probability. This will involve analyzing the output of the combinatorial search algorithm under bounded perturbations and will be incorporated into Section 5.1. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper describes a two-stage procedure: a novel identification algorithm that integrates multiple partial-observation trajectories to produce estimates of the unknown LTI system, followed by adaptation of a classic sensor-allocation routine applied to those estimates. Non-asymptotic guarantees are asserted for the end-to-end result. No quoted step reduces a claimed prediction or uniqueness result to a fitted parameter, self-citation, or definitional tautology; the identification and allocation stages remain distinct and rely on external observability concepts rather than importing load-bearing premises from the authors' prior work.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only abstract available so ledger is minimal and based solely on explicit statements; full paper may contain additional fitted parameters or assumptions.

axioms (2)
  • domain assumption The system is linear and time-invariant.
    Central focus of the paper on linear systems with observability.
  • domain assumption Multiple trajectories with varying sensor subsets are available for data collection.
    Required for the first-stage identification algorithm.

pith-pipeline@v0.9.0 · 5652 in / 1232 out tokens · 45495 ms · 2026-05-20T15:41:14.512034+00:00 · methodology

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