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An adaptive data sampling strategy for stabilizing dynamical systems via controller inference

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that iteratively using freshly inferred low-dimensional stabilizing controllers to generate the next input signal yields data sets that are provably informative for stabilization and minimal in size, cutting model queries…

desk verdict The ICI algorithm is a genuine new idea with credible empirical gains, but the 'provably minimal-size' claim in the abstract is not backed by the theory for the algorithm as implemented. read the letter →

arxiv 2506.01816 v2 pith:BLVO2CZY submitted 2025-06-02 math.OC cs.LGcs.NAmath.DSmath.NA

Steffen W. R. Werner , Benjamin Peherstorfer This is my paper
classification math.OCcs.LGcs.NAmath.DSmath.NA MSC 37N3565F5590C2290C5993B52
keywords adaptivedatasamplingcontrollerinferenceinformativityfeedbackstabilizationnonlineardynamicalsystemslow-dimensionalsubspacesinformativedata-drivencontrol
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

This paper aims to solve a chicken-and-egg problem in data-driven control: to learn a stabilizing controller you need data from the unstable system, but unstable trajectories grow or oscillate so fast that the data becomes useless. The proposed iterative controller inference (ICI) scheme breaks the loop by using each freshly inferred low-dimensional controller as the input generator for the next system query, so data are collected while the system is already being pushed toward the steady state. Under precise assumptions the resulting data sets are provably informative for stabilization and minimal in size, with a worst-case bound of n_min iterations (or n_min + p under weaker rank assumptions). In experiments on heat flow, a power network, a tubular reactor, a crystal-cluster model, and flow behind an obstacle, ICI needs between 1.5 and 25 times fewer system queries than non-adaptive low-dimensional controller inference with random inputs, and in one case it stabilizes a system the baseline cannot stabilize at all.

What carries the argument

The central object is the data triplet (U^n, X^n, Y^n) together with the iteratively expanded subspace V_j and the low-dimensional controller inference step (Algorithm 1). The load-bearing identity is the sufficient condition of Lemma 2: if inputs are chosen as U = KX with K stabilizing over the trajectory subspace V_min, then the projected closed-loop matrix \hat{Y} \hat{X}^\dagger = \hat{A} + \hat{B} \hat{K} inherits the stability of K, so the data are informative for stabilization over V_min. Iterating this over nested subspaces is the ICI algorithm (Algorithm 2), with a re-projection scheme (Algorithm 3) used to keep the projected data well-conditioned and to satisfy the same-controller premise of Theorem 2.

What would settle it

Run ICI on a linear discrete-time system with known intrinsic dimension n_min, using the re-projection variant that is meant to satisfy the same-controller assumption, and count the system queries needed to produce a stabilizing controller. If the method requires more than n_min queries, or if the resulting data triplet fails the informativity conditions of Proposition 1, the minimal-data theorem is false.

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Extended reading notes

Core claim

The central discovery is that a feedback-driven data sampling strategy turns the task of stabilizing an unknown nonlinear system into a sequence of low-dimensional controller inference problems over nested subspaces V_1 ⊆ V_2 ⊆ ... . The input used for each new query is generated by the controller inferred in the previous step, u(t) = K_{j-1}(x(t) - \bar{x}) + \bar{u}. The paper proves (Lemma 2, Theorem 1, Theorem 2) that if the states stay near the steady state and the previous controller stabilizes the projected system over the extended subspace, then the accumulated data triplet is informative for stabilization over that subspace, and once the subspace reaches the intrinsic dimension n_min, the inferred controller locally stabilizes the original nonlinear system. The proof machinery is the data-informativity condition for low-dimensional subspaces: the projected data (U, V^\top X, V^\top Y) must satisfy a linear-matrix-inequality (or eigenvalue) condition, and the stabilizing choice of inputs guarantees that the projected closed-loop matrix is stable, so the size of the data set scales with the subspace dimension rather than the full state dimension.

Load-bearing premise

The theorem that guarantees a minimal, informative data set assumes the controller from the previous step already stabilizes the system on the larger subspace that contains the new data sample; the authors note that the algorithm as presented does not actually generate all its inputs with that same controller, so the guarantee applies to a variant of the method rather than the exact implementation.

Editorial extensions

If this is right

  • The adaptive scheme suppresses dynamical instabilities during data collection, keeping trajectories near the steady state so that linearization-based controller inference stays meaningful.
  • Under the theorem's assumptions, the data sets produced are provably informative for stabilization and minimal in size, so the number of system queries scales with the intrinsic system dimension rather than the full state dimension.
  • Convergence is guaranteed: the method terminates with a locally stabilizing controller after at most n_min + p iterations under the rank conditions of Corollary 1, and after n_min iterations under the stronger premises of Theorem 2.
  • Numerical experiments show that ICI uses 1.5 to 25 times fewer model queries than unguided random-input sampling, and can stabilize systems, such as the Brazilian power network, where the baselines failed within hundreds of queries.
  • The approach opens the door to stabilizing systems in edge cases and limit states where instabilities arise and data collection is inherently difficult, as claimed in the abstract.
  • The method relies only on forward evaluations of the model, making it compatible with existing simulation and query infrastructures.
  • When re-projection is used, the number of data samples in the re-projected set can be reduced from T to r, improving conditioning and lowering computational cost.
  • The same algorithmic pattern may extend to other data-driven tasks where informative data is needed while the system must be kept stable during collection.

Reading between the lines

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

  • The same feedback-driven sampling principle could be applied to other data-driven tasks, such as system identification or prediction, where closed-loop data generation might bias but also condition the data favorably.
  • The re-projection scheme that samples along the subspace basis with controller-generated inputs may be of independent value for conditioning data in low-dimensional controller inference, beyond the ICI loop.
  • A testable extension is to quantify the probability that random inputs meet the persistent-excitation condition versus the ICI inputs, since random inputs are generic but not minimal, and the gap between the two is likely to grow with the state dimension.
  • The minimality guarantee would be most fragile when the subspace extension introduces a new unstable direction not stabilized by the previous controller; experiments suggest this fragility is manageable, but a systematic study on systems with many unstable modes would clarify the limits.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes an adaptive data sampling scheme, called iterative controller inference (ICI), for generating informative data for stabilizing nonlinear dynamical systems from scarce data. The method alternates between (i) querying the system using the most recently inferred low-dimensional feedback controller and (ii) extending a nested sequence of subspaces and re-inferring a controller over the extended subspace via low-dimensional data-informative controller inference. The paper claims that, under mild assumptions, the approach provably generates data sets that are informative for stabilization and have minimal size, and it reports numerical experiments on several large-scale examples, including a power network and a laminar flow problem, showing reductions in the number of model queries by factors up to 25 compared with unguided random-excitation data generation. The theoretical results are Lemma 1/2 and Theorems 1--3, which give conditional guarantees about informative data when a stabilizing controller is already available or when the previous controller stabilizes the extended subspace.

Significance. If the main claim were fully established, this would be a valuable contribution: it addresses a practically important bottleneck in data-driven control, namely that unstable systems produce unusable trajectories during data collection, and it provides an algorithmic way to collect informative data while stabilizing the system. The numerical experiments cover diverse and challenging examples, the source code and data are openly available, and the conditional theoretical results (Lemma 2, Theorems 1 and 3) are internally consistent. However, the central provable-minimality claim for the actual ICI algorithm is not established: Theorem 2 assumes exactly the property that the algorithm is trying to construct, and the authors explicitly concede this in Section 3.3. The paper is therefore best assessed as an empirically promising method with sound but incompletely connected theoretical scaffolding.

major comments (3)
  1. [Section 3.3, Theorem 2] Theorem 2 assumes that K_{j-1} locally stabilizes the projected system over the extended subspace V_j and that the input samples U_j^n are generated columnwise by that same K_{j-1}. In Algorithm 2, at iteration j, the control input is generated by K_{j-1} before V_j is formed (Line 11), and K_{j-1} was inferred from the previous subspace V_{j-1} only. Thus the theorem's key assumption is not satisfied by the algorithm as presented. The authors themselves state in Section 3.3: "in the ICI method as presented in Section 3.1, the assumption that the same K_{j-1} has been used for the generation of U_j^n will not be satisfied since the controller is updated in every step." Consequently, Theorem 2 does not support the abstract's claim that the approach "provably generates data sets that are informative for stabilization and have minimal size." The pointer to Section 3.5 does not close this gap: Algorithm 3 is invoked only when no stabilizing K_j is found (Algorithm 2, Lines 17--19) and still requires a supplied K that stabilizes over V, which is exactly the property that is not known at that point.
  2. [Section 3.3, Corollary 1] Corollary 1 is the only formal result that does not assume the existence of a stabilizing K_{j-1}, but its guarantee is conditional on the concatenated matrix [eX_j^T U_j^T]^T having full column rank for all j = 1, ..., n_min + p. The paper does not prove that this rank condition holds for Algorithm 2; the proof only cites "the sampling number for system identification over low-dimensional subspaces." With feedback-generated inputs, persistence of excitation is nontrivial, as the paper itself notes in Remark 1. As stated, Corollary 1 is an assumption-based bound rather than a guarantee about the ICI algorithm, so it cannot serve as the rigorous foundation for the claimed worst-case n_min + p step termination.
  3. [Sections 3.2 and 3.5, Theorems 1 and 3] The minimal-data results all assume that a stabilizing controller K is already available: Lemma 2 and Theorem 1 require K to stabilize the linearization, and Theorem 3 assumes that K is locally stabilizing over V. Since the paper's task is precisely to construct such a controller, these results show that a stabilizing controller can generate minimal-size informative data, but they do not by themselves prove that the controllers produced by the ICI iteration have that property. The authors acknowledge the causal gap in Section 3.2, but the abstract and conclusions still state the provable-minimality claim without this caveat. The paper should either restrict the formal claims to the idealized setting or provide a convergence argument that does not presuppose the stabilizing controller.
minor comments (5)
  1. [Lemma 2 proof] In the proof of Lemma 2, "B×R^{N×p}" should be "B ∈ R^{N×p}".
  2. [Theorem 1 proof] In the proof of Theorem 1, "the the shifted data" contains a duplicated article.
  3. [Algorithm 2] Algorithm 2 does not specify what K_j is assigned when Algorithm 1 fails to find a stabilizing controller and before Algorithm 3 is applied; this matters because K_j is used at the next iteration to generate the control signal.
  4. [Section 3.4] The sentence "This happens eventually after p additional steps under the assumption that the state samples are linearly independent" is imprecise: linear independence of state samples alone does not guarantee identifiability when the inputs are generated by feedback; a more specific condition or reference is needed.
  5. [Abstract and Figure 1] The abstract says the method uses "up to one order of magnitude fewer data samples," but Figure 1 reports improvement factors up to 25, which is more than one order of magnitude; the phrasing should be aligned with the reported factors.

Circularity Check

2 steps flagged · score 4.0 of 10

The formal minimal-size guarantee assumes the very stabilizing-controller property the iteration seeks; the paper explicitly concedes the mismatch, making this an acknowledged conditional gap and partial self-citation load rather than a fully circular derivation.

  1. self definitional [Section 3.3, Theorem 2 and its discussion; Section 3.4, Algorithm 2, lines 10-16]
    "We note that Theorem 2 critically relies on the assumption that K_{j-1} stabilizes over the subspace V_j. If this assumption does not hold, then our ICI method is still applicable but it is not guaranteed to give a minimal data set. Furthermore, considering the assumptions made in Theorem 2, we have to note that in the ICI method as presented in Section 3.1, the assumption that the same K_{j-1} has been used for the generation of U^n_j will not be satisfied since the controller is updated in every step of the method."

    Theorem 2 concludes that the data triplet is informative for stabilization over V_j, and that with j=n_min the inferred controller locally stabilizes the system. But the theorem's premise is exactly that K_{j-1} already locally stabilizes the projected system over the extended subspace V_j and that all inputs U^n_j were generated by that same K_{j-1}. In the implemented ICI (Algorithm 2), V_j is extended using x(t_{j-1})-bar{x} after sampling with K_{j-1}, and K is updated every iteration, so the premise is not met. The conclusion is therefore a restatement of the assumption rather than a derivation from the algorithm's actual operation; the paper's own 'provably ... minimal size' claim is not established for the method as run.

  2. self citation load bearing [Section 3.2, paragraph before Lemma 2; Section 2.3, Proposition 2]
    "It has been shown in [43, Cor. 5] that the minimal number of samples required for an informative data set is the intrinsic dimension n_min of the system and it has been shown that such data sets exist. The key step of the proof of [43, Cor. 5] is the construction of a suitable input signal using a stabilizing controller."

    The paper's central 'minimal size' benchmark (n_min samples) is imported from the authors' own prior paper [43], and the key constructive step in that cited result is itself the construction of an input signal using a stabilizing controller—the same premise that the present Theorem 2 assumes. Thus the provable-minimality chain in this paper inherits both the self-citation and the circular input-design premise from [43]. The cited work is a published, independent theorem, so this is load-bearing self-citation rather than a concealed equivalence, but it does not provide an external check on the central assumption.

full rationale

The adaptive sampling scheme, the iterative controller-inference algorithm, and the numerical comparisons against external benchmark problems (heat flow, Brazilian power network, tubular reactor, crystal cluster, Navier-Stokes obstacle flow) are new and self-contained empirical contributions; they do not reduce to the paper's own fitted values or circular definitions. The main concern is the formal guarantee advertised in the abstract. Theorem 2 proves data informativity and minimal size only under the assumption that the previous controller K_{j-1} locally stabilizes the projected system over the extended subspace V_j and that all inputs were generated by that same controller. In Algorithm 2 the controller is updated every iteration and V_j is extended after sampling, so the assumption is not satisfied; the authors state this explicitly. Consequently, the 'provably ... minimal size' claim is an overstatement relative to the implemented method, and the theoretical chain is conditional on exactly the property the iteration is intended to construct. The n_min minimal-sample result and the nonlinear extension are also taken from the authors' prior work [42,43], whose key construction uses the same stabilizing-controller-as-input premise. These are published results with independent content, so the circularity is partial rather than total: the provable-minimality argument does not close for the actual algorithm, but the numerical conclusions are supported by external test cases and open-source code. Score 4 reflects this mix of acknowledged conditional circularity and substantial independent numerical content.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the linearization assumption, rank conditions on sampled data, and the critical premise that the previous controller stabilizes the extended subspace. The latter is not guaranteed by the algorithm and is essentially the property being sought. No new physical entities are introduced.

free parameters (3)
  • state scaling alpha
    Algorithm 3 uses alpha > 0 to scale sampled states relative to the steady state; it controls how close data stays to the linearization point. Values are not reported for any experiment, yet the informativity and stabilization results depend on this proximity.
  • random input variance
    Initial data and fallback re-projection use normally distributed random inputs around the steady-state control, but the variance is not specified; it affects how quickly trajectories leave the linearization region and thus the comparison against baselines.
  • orthogonalization tolerance
    Section 4.2 compares small and large orthogonalization tolerances; the choice changes whether re-projections are triggered and the reliability of subspace expansion, but the algorithm does not state a default.
assumptions (4)
  • domain assumption The model f is analytic so the linearization (7) approximates local dynamics; controlled trajectories stay within a small epsilon of the steady state (Theorem 1, Theorem 2).
    Needed to justify using linearized data; the algorithm tries to enforce small epsilon via alpha but provides no quantitative bound.
  • domain assumption The shifted state data eX has row rank n_min (Theorem 1) and the concatenated matrix [eX^T U^T]^T has full column rank (Corollary 1).
    The rank conditions are assumed, not shown to be produced by ICI; they are the standard informativity assumptions.
  • ad hoc to paper K_{j-1} locally stabilizes the projected system over the extended subspace V_j (Theorem 2).
    The paper acknowledges this is not satisfied by the algorithm as presented; it is the key unproved premise behind the minimal-data guarantee.
  • standard math Prior results: data informativity characterization (Prop 1, from [39,43]) and nonlinear informativity transfer (Prop 2, from [43]; Cor 1 from [42]).
    These are published theorems the paper builds on; they are from the authors' own prior work and are not re-proved here.

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Cite this review

Pith. "Pith review of An adaptive data sampling strategy for stabilizing dynamical systems via controller inference." pith.science (2026). https://pith.science/paper/BLVO2CZY

@misc{pith2026250601816,
  author       = {Pith},
  title        = {Pith review of: An adaptive data sampling strategy for stabilizing dynamical systems via controller inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BLVO2CZY}},
  note         = {Machine review of arXiv:2506.01816}
}
read the original abstract

Learning stabilizing controllers from data is an important task in engineering applications; however, collecting informative data is challenging because unstable systems often lead to rapidly growing or erratic trajectories. In this work, we propose an adaptive sampling scheme that generates data while simultaneously stabilizing the system to avoid instabilities during the data collection. Under mild assumptions, the approach provably generates data sets that are informative for stabilization and have minimal size. The numerical experiments demonstrate that controller inference with the novel adaptive sampling approach learns controllers with up to one order of magnitude fewer data samples than unguided data generation. The results show that the proposed approach opens the door to stabilizing systems in edge cases and limit states where instabilities often occur and data collection is inherently difficult.

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Works this paper leans on

48 extracted references · 30 canonical work pages

  1. [1]

    A. C. Antoulas, I. V. Gosea, and A. C. Ionita. Model reduction of bilinear systems in the Loewner framework.SIAM J. Sci. Comput., 38(5):B889–B916, 2016.doi: 10.1137/15M1041432

    doi:10.1137/15m1041432 2016

  2. [2]

    M. Behr, P. Benner, and J. Heiland. Example setups of Navier-Stokes equations with control and observation: Spatial discretization and representation via linear- quadratic matrix coefficients. e-print arXiv:1707.08711, arXiv, 2017. Mathematical Software (cs.MS).doi:10.48550/arXiv.1707.08711

    work page Pith review arXiv doi:10.48550/arxiv.1707.08711 2017

  3. [3]

    Berman and B

    J. Berman and B. Peherstorfer. CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations.Proceedings of the 41st International Conference on Machine Learning, PMLR, 235:3565–3584,

    work page

  4. [4]

    Boull´ e and A

    N. Boull´ e and A. Townsend. Learning elliptic partial differential equations with randomized linear algebra.Found. Comput. Math., 23(2):709–739, 2023.doi:10. 1007/s10208-022-09556-w

    work page 2023

  5. [5]

    S. L. Brunton, J. L. Proctor, and J. N. Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems.Proc. Natl. Acad. Sci. U. S. A., 113(15):3932–3937, 2016.doi:10.1073/pnas.1517384113

    doi:10.1073/pnas.1517384113 2016

  6. [6]

    M. C. Campi, A. Lecchini, and S. M. Savaresi. Virtual reference feedback tuning: a direct method for the design of feedback controllers.Automatica J. IF AC, 38(8):1337– 1346, 2002.doi:10.1016/S0005-1098(02)00032-8. Preprint. 2026-02-10 S. W. R. Werner, B. Peherstorfer: Adaptive data sampling for control24 0 1 2 3 4 5 6 7 8 9 10−0.5 0 0.5 1 1.5 time τ ·t o...

    work page doi:10.1016/s0005-1098(02)00032-8 2002

  7. [7]

    Power system examples

    Cepel. Power system examples. hosted at MORwiki – Model Order Reduction Wiki,

    work page

  8. [8]

    De Persis and P

    C. De Persis and P. Tesi. Formulas for data-driven control: Stabilization, optimality, and robustness.IEEE Trans. Autom. Control, 65(3):909–924, 2020.doi:10.1109/ TAC.2019.2959924

    arXiv 2020

Show all 48 references
  1. [9]

    Fliess and C

    M. Fliess and C. Join. Model-free control.Int. J. Control, 86(12):2228–2252, 2013. doi:10.1080/00207179.2013.810345

    2013

  2. [10]

    Freitas, J

    F. Freitas, J. Rommes, and N. Martins. Gramian-based reduction method applied to large sparse power system descriptor models.IEEE Trans. Power Syst., 23(3):1258– 1270, 2008.doi:10.1109/TPWRS.2008.926693

    2008

  3. [11]

    I. V. Gosea and A. C. Antoulas. Data-driven model order reduction of quadratic- bilinear systems.Numer. Linear Algebra Appl., 25(6):e2200, 2018.doi:10.1002/ nla.2200. Preprint. 2026-02-10 S. W. R. Werner, B. Peherstorfer: Adaptive data sampling for control25

    2018

  4. [12]

    M. C. Grant and S. P. Boyd. Graph implementations for nonsmooth convex programs. In V. D. Blondel, S. P. Boyd, and H. Kimura, editors,Recent Advances in Learning and Control, volume 371 ofLect. Notes Control Inf. Sci., pages 95–110. Springer, London, 2008.doi:10.1007/978-1-848...

    doi

  5. [13]

    M. C. Grant and S. P. Boyd. CVX: Matlab software for disciplined convex program- ming, version 2.2.http://cvxr.com/cvx, January 2020

    2020

  6. [14]

    Hambly, R

    B. Hambly, R. Xu, and H. Yang. Policy gradient methods for the noisy linear quadratic regulator over a finite horizon.SIAM J. Control Optim., 59(5):3359–3391, 2021.doi:10.1137/20M1382386

    2021 doi

  7. [15]

    R. F. Heinemann and A. B. Poore. Multiplicity, stability, and oscillatory dy- namics of the tubular reactor.Chem. Eng. Sci., 36(9):1411–1419, 1981.doi: 10.1016/0009-2509(81)80175-3

    1981 doi

  8. [16]

    Kramer and K

    B. Kramer and K. E. Willcox. Nonlinear model order reduction via lifting trans- formations and proper orthogonal decomposition.AIAA J., 57(6):2297–2307, 2019. doi:10.2514/1.J057791

    2019 doi

  9. [17]

    Krauth, S

    K. Krauth, S. Tu, and B. Recht. Finite-time analysis of approximate policy iteration for the linear quadratic regulator. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d’Alch´ e Buc, E. Fox, and R. Garnett, editors,Advances in Neural Information Processing Systems, volume 32...

    2019

  10. [18]

    Leibfritz.COM P l eib:COnstrainedMatrix-optimizationProblemlibrary – a collection of test examples for nonlinear semidefinite programs, control system design and related problems

    F. Leibfritz.COM P l eib:COnstrainedMatrix-optimizationProblemlibrary – a collection of test examples for nonlinear semidefinite programs, control system design and related problems. Tech.-report, University of Trier, 2004. URL:http://www. friedemann-leibfritz.de/COMPlib_Data/...

    2004

  11. [19]

    Lequin, M

    O. Lequin, M. Gevers, M. Mossberg, E. Bosmans, and L. Triest. Iterative feedback tuning of PID parameters: comparison with classical tuning rules.Control Eng. Pract., 11(9):1023–1033, 2003.doi:10.1016/S0967-0661(02)00303-9

    2003 doi

  12. [20]

    Losekann, G

    L. Losekann, G. A. Marrero, F. J. Ramos-Real, and E. L. F. De Almeida. Efficient power generating portfolio in Brazil: Conciliating cost, emissions and risk.Energy Policy, 62:301–314, 2013.doi:10.1016/j.enpol.2013.07.049

    2013 doi

  13. [21]

    A. J. Mayo and A. C. Antoulas. A framework for the solution of the generalized realization problem.Linear Algebra Appl., 425(2–3):634–662, 2007. Special issue in honor of P. A. Fuhrmann, Edited by A. C. Antoulas, U. Helmke, J. Rosenthal, V. Vinnikov, and E. Zerz.doi:10.1016/j....

    2007 doi

  14. [22]

    The MOSEK optimization toolbox for MATLAB manual

    MOSEK ApS. The MOSEK optimization toolbox for MATLAB manual. Ver- sion 9.1.9, November 2019. URL:https://docs.mosek.com/9.1/toolbox/index. html

    2019

  15. [23]

    Nijmeijer and A

    H. Nijmeijer and A. Van der Schaft.Nonlinear Dynamical Control Systems. Springer, New York, NY, fourth edition, 2016.doi:10.1007/978-1-4757-2101-0

    2016 doi

  16. [24]

    Peherstorfer

    B. Peherstorfer. Sampling low-dimensional Markovian dynamics for preasymptotically recovering reduced models from data with operator inference.SIAM J. Sci. Comput., 42(5):A3489–A3515, 2020.doi:10.1137/19M1292448. Preprint. 2026-02-10 S. W. R. Werner, B. Peherstorfer: Adaptive ...

    2020 doi

  17. [25]

    Peherstorfer, S

    B. Peherstorfer, S. Gugercin, and K. Willcox. Data-driven reduced model construction with time-domain Loewner models.SIAM J. Sci. Comput., 39(5):A2152–A2178, 2017. doi:10.1137/16M1094750

    2017 doi

  18. [26]

    Peherstorfer and K

    B. Peherstorfer and K. Willcox. Data-driven operator inference for nonintrusive projection-based model reduction.Comput. Methods Appl. Mech. Eng., 306:196–215, 2016.doi:10.1016/j.cma.2016.03.025

    2016 doi

  19. [27]

    J. C. Perdomo, J. Umenberger, and M. Simchowitz. Stabilizing dynamical systems via policy gradient methods. In M. Ranzato, A. Beygelzimer, Y. Dauphin, P. S. Liang, and J. Wortman Vaughan, editors,Advances in Neural Information Processing Systems, volume 34, pages 29274–29286, 2021

    2021

  20. [28]

    M. G. Safonov and T.-C. Tsao. The unfalsified control concept: A direct path from experiment to controller. In B. .A Francis and A. R. Tannenbaum, editors,Feedback Control, Nonlinear Systems, and Complexity, volume 202 ofLect. Notes Control Inf. Sci., pages 196–214. Springer, ...

    1995 doi

  21. [29]

    Schaeffer, G

    H. Schaeffer, G. Tran, and R. Ward. Extracting sparse high-dimensional dynamics from limited data.SIAM J. Appl. Math., 78(6):3279–3295, 2018.doi:10.1137/ 18M116798X

    2018

  22. [30]

    P. J. Schmid. Dynamic mode decomposition of numerical and experimental data.J. Fluid Mech., 656:5–28, 2010.doi:10.1017/S0022112010001217

    2010 doi

  23. [31]

    Schulze and B

    P. Schulze and B. Unger. Data-driven interpolation of dynamical systems with delay. Syst. Control Lett., 97:125–131, 2016.doi:10.1016/j.sysconle.2016.09.007

    2016 doi

  24. [32]

    Schulze, B

    P. Schulze, B. Unger, C. Beattie, and S. Gugercin. Data-driven structured realization. Linear Algebra Appl., 537:250–286, 2018.doi:10.1016/j.laa.2017.09.030

    2018 doi

  25. [33]

    L. F. Shampine and M. W. Reichelt. The MATLAB ODE Suite.SIAM J. Sci. Comput., 18(1):1–22, 1997.doi:10.1137/S1064827594276424

    1997 doi

  26. [34]

    Swischuk, B

    R. Swischuk, B. Kramer, C. Huang, and K. Willcox. Learning physics-based reduced- order models for a single-injector combustion process.AIAA J., 58(6):2658–2672, 2020.doi:10.2514/1.J058943

    2020 doi

  27. [35]

    M. Toda. Vibration of a chain with nonlinear interaction.J. Phys. Soc. Jpn., 22(2):431–436, 1967.doi:10.1143/JPSJ.22.431

    1967 doi

  28. [36]

    J. H. Tu, C. W. Rowley, D. M. Luchtenburg, S. L. Brunton, and J. N. Kutz. On dynamic mode decomposition: Theory and applications.J. Comput. Dyn., 1(2):391– 421, 2014.doi:10.3934/jcd.2014.1.391

    2014 doi

  29. [37]

    Van Overschee and B

    P. Van Overschee and B. De Moor.Subspace Identification for Linear Systems: The- ory, Implementation, Applications. Springer, Boston, MA, 1996.doi:10.1007/ 978-1-4613-0465-4

    1996

  30. [38]

    H. J. Van Waarde, J. Eising, M. K. Camlibel, and H. L. Trentelman. The informativity approach: To data-driven analysis and control.IEEE Control Syst., 43(6):32–66, 2023.doi:10.1109/MCS.2023.3310305. Preprint. 2026-02-10 S. W. R. Werner, B. Peherstorfer: Adaptive data sampling ...

    2023

  31. [39]

    H. J. Van Waarde, J. Eising, H. L. Trentelman, and M. K. Camlibel. Data informa- tivity: A new perspective on data-driven analysis and control.IEEE Trans. Autom. Control, 65(11):4753–4768, 2020.doi:10.1109/TAC.2020.2966717

    2020

  32. [40]

    S. W. R. Werner.Structure-Preserving Model Reduction for Mechanical Systems. Dissertation, Otto-von-Guericke-Universit¨ at, Magdeburg, Germany, 2021.doi:10. 25673/38617

    2021

  33. [41]

    An adaptive data sampling strategy for stabilizing dynamical systems via controller inference

    S. W. R. Werner. Code, data and results for numerical experiments in “An adaptive data sampling strategy for stabilizing dynamical systems via controller inference” (version 1.0), June 2025.doi:10.5281/zenodo.8183173

    2025 doi

  34. [42]

    S. W .R. Werner and B. Peherstorfer. Context-aware controller inference for stabi- lizing dynamical systems from scarce data.Proc. R. Soc. A: Math. Phys. Eng. Sci., 479(2270):20220506, 2023.doi:10.1098/rspa.2022.0506

    2023

  35. [43]

    S. W .R. Werner and B. Peherstorfer. On the sample complexity of stabilizing linear dynamical systems from data.Found. Comput. Math., 24(3):955–987, 2024.doi: 10.1007/s10208-023-09605-y

    2024 doi

  36. [44]

    S. W. R. Werner and B. Peherstorfer. System stabilization with policy optimization on unstable latent manifolds.Comput. Methods Appl. Mech. Eng., 433, Part A:117483, 2025.doi:10.1016/j.cma.2024.117483

    2025

  37. [45]

    J. C. Willems, P. Rapisarda, I. Markovsky, and B. L. M. De Moor. A note on persistency of excitation.Syst. Control Lett., 54(4):325–329, 2005.doi:10.1016/j. sysconle.2004.09.003

    2005 doi

  38. [46]

    Y. B. Zhou.Model Reduction for Nonlinear Dynamical Systems with Parametric Uncertainties. PhD thesis, Massachusetts Institute of Technology, Cambridge, Mas- sachusetts, USA, 2012. URL:http://hdl.handle.net/1721.1/77118. Preprint. 2026-02-10

    2012

  39. [2008]

    URL:http://modelreduction.org/index.php/Power_system_examples

  40. [2024]

    URL:https://proceedings.mlr.press/v235/berman24b.html

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.