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REVIEW 4 major objections 6 minor 60 references

Koopman-Based Event-Triggered Control from Data

T0 review · 4 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Using one dataset, two LMIs, and a Koopman lift, the paper designs a state-feedback gain and an event-triggering threshold that make the lifted closed loop of a discrete-time nonlinear system exponentially stable in the Lyapunov sense.

desk verdict A legitimate empirical combination with a load-bearing theoretical gap: the Lyapunov guarantee is proved only for an assumed-exact lifted model, and the printed LMI has a concrete fixable error. read the letter →

arxiv 2504.14334 v1 pith:GB2RWBOF submitted 2025-04-19 eess.SY cs.SY

Zeyad M. Manaa , Ayman M. Abdallah , Mohamed Ismail , Samil El Ferik This is my paper · ORCID
classification eess.SYcs.SY MSC 93C6593C5593B3037N3593C10
keywords event-triggeredcontroldata-drivenKoopmanoperatordiscrete-timenonlinearsystemsLyapunovstabilitylinearmatrixinequalitieszero-orderhold
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 is trying to establish a direct data-driven route to event-triggered control for discrete-time nonlinear systems whose equations are unknown. Instead of identifying the plant, the method lifts measured states through a chosen dictionary of observables, $\Xi(x)$, so that the dynamics look linear in a higher-dimensional Koopman space, and then designs both the feedback gain and the triggering threshold from a single dataset by solving LMIs. Theorems 1 and 2 state that the resulting controller exponentially stabilizes the lifted closed loop in the Lyapunov sense with a prescribed rate $\alpha$, while the event-triggering policy reduces communication instances relative to time-triggered control. If true, this would turn event-triggered control for a class of nonlinear plants into a convex, data-only design problem, which is why the paper matters.

What carries the argument

The load-bearing construction is the Koopman-lifted, data-driven closed-loop representation of Lemma 1. With the Koopman operator understood as the linear evolution $K_t\xi=\xi\circ f$ on observable functions, the paper chooses a finite dictionary $\Xi(x)$, so the controlled plant is approximated by $z_{k+1}=Az_k+Bu_k$; then, under the full-row-rank assumption, the identities $\begin{bmatrix} I \\ K \end{bmatrix}=\begin{bmatrix} Z_0 \\ U_0 \end{bmatrix}L$ and $\begin{bmatrix} 0 \\ K \end{bmatrix}=\begin{bmatrix} Z_0 \\ U_0 \end{bmatrix}N$ let the event-triggered loop be written as $z_{k+1}=Z_1Lz_k+Z_1Ne_k$, with no $\{A,B\}$ appearing. This representation carries the argument because it converts both tasks into LMIs: Theorem 1 finds $G_1$ through a Schur-complement condition to obtain $K$, and Theorem 2 uses the S-procedure to maximize $\gamma$ subject to the Lyapunov condition, with everything expressed directly in the collected data matrices.

What would settle it

Take the polynomial plant of Example 2 with a degree-6 monomial dictionary (or any dictionary with visible closure error), learn $K$ and $\gamma$ by the algorithm, simulate the original nonlinear plant with the event-triggered zero-order hold, and record $V(k+1)/V(k)$ along the trajectory; a single time instant at which this ratio exceeds $\alpha$ while $\|e_k\|\le\gamma\|z_k\|$ would falsify the transfer of stability from the lifted model to the plant.

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Extended reading notes

Core claim

The central claim is that the pair of design objects can be computed straight from data, with no explicit identification of $A$ and $B$: after collecting $U_0$, $Z_0=\Xi(X_0)$, and $Z_1=\Xi(X_1)$, one solves the LMI in Theorem 1 for $G_1$ to get $K=U_0G_1(Z_0G_1)^{-1}$, and then solves the LMI in Theorem 2 for the largest threshold $\gamma$ that keeps the Lyapunov inequality satisfied whenever $\|e_k\|\le\gamma\|z_k\|$. The closed loop is written in the data-driven form $z_{k+1}=Z_1Lz_k+Z_1Ne_k$, and Theorem 2 guarantees exponential stability with rate $\alpha$ along event-triggered trajectories. The paper presents three simulations: a slow-manifold system that admits an exact Koopman linearization, a polynomial system that exhibits the closure problem with finite dictionaries, and a linear system that recovers the existing data-driven event-triggered result as a special case.

Load-bearing premise

The guarantee transfers from the lifted linear model to the true nonlinear plant only if the chosen observables represent the plant well enough to make the data-computed Lyapunov certificate valid for the actual system, and the paper provides no quantitative error bound for that transfer.

Editorial extensions

If this is right

  • If the lifted model is faithful, no identification step is needed: one dataset fixes both the control law and the scheduling rule.
  • The triggering rule preserves the exponential decay rate $\alpha$ of the lifted closed loop while updating $u_k$ only when the relative lifted-state error crosses $\gamma$.
  • In the exactly linearizable test case the method matches known Koopman-control behavior and cuts communication events by roughly 40 percent in simulation.
  • In the approximate (closure-error) case, the steady-state error depends systematically on the dictionary degree, decreasing from degree 1 through 5 and rising again at degree 6, so dictionary size alone does not guarantee better performance.
  • With identity observables the algorithm reduces to the existing data-driven event-triggered design for linear systems, giving a consistency check.

Reading between the lines

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

  • Going beyond the paper: the proven exponential stability is for the lifted model; turning it into a guarantee for the original plant would require an explicit bound on the Koopman closure residual $z_{k+1}-(Az_k+Bu_k)$, and such a bound could turn the method into a robust data-driven event-triggered control design.
  • A natural testable extension is to compute a guaranteed positive minimum inter-event time from the data matrices and enforce it, since the paper does not analyze dwell time between transmissions.
  • Because the trigger is evaluated in lifted coordinates, $\|e^\xi_k\|\le\gamma\|\xi(x_k)\|$, a designer choosing this scheme implicitly weights observable components rather than original states; an alternative threshold on $\|x_k-x_{k_i}\|$ would be a different policy and could be compared experimentally on the same data.
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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

4 major / 6 minor

Summary. The paper proposes a data-driven event-triggered control method for discrete-time nonlinear systems. It lifts the state via a dictionary of observable functions xi(x), assumes the lifted dynamics are approximately linear, z_{k+1} = A z_k + B u_k, and then designs a static feedback gain K and a relative triggering threshold gamma by solving LMIs derived from Lyapunov-based arguments. The main results are Theorem 1 (controller gain from data), Theorem 2 (threshold computation), and Algorithm 1, validated on three simulation examples including a nonlinear polynomial system. The paper claims exponential stability in the Lyapunov sense with reduced communication compared to time-triggered control.

Significance. If the stability guarantee could be transferred to the original nonlinear plant, the contribution would be a useful direct data-driven event-triggered design for nonlinear systems. The paper demonstrates the idea in simulations with up to 40% communication reduction and gives a concrete algorithm. The strengths are the problem formulation, the explicit LMI-based procedure, and the attempt to combine Koopman lifting with event-triggered data-driven control. However, as written, the analysis applies only to the lifted linear model and has several technical gaps, including an incorrect LMI in Theorem 1, a reversed S-procedure step in Theorem 2, and no approximation-error bound to relate the lifted model to the original plant. The paper does not provide code or machine-checked proofs, so the value depends on correcting these gaps.

major comments (4)
  1. [Section 3.2, Lemma 1 and Eq. (15)] The data-driven representation identifies z_{k+1} = Z1 L z_k + Z1 N e_k by using the equality [A B][Z0; U0] = Z1 in the proof. This equality holds only if the finite-dimensional Koopman model (12) is exact on the data. For a generic observable dictionary, the per-step residual R_k = xi(x_{k+1}) - (A xi(x_k) + B u_k) is nonzero, as Example 2's closure problem (Section 4.2) concedes. The actual closed loop under the designed controller is z_{k+1} = Z1 L z_k + Z1 N e_k + R_k, and no bound on R_k is given anywhere in Sections 3.1-3.4. Consequently, the Lyapunov inequality (16) and Theorems 1-2 do not imply exponential stability of the original nonlinear plant (1). The authors need to state an explicit bound on the lifting/closure error and incorporate it into the stability analysis, or explicitly restrict the paper's claims to the exact-lifting case.
  2. [Section 3.3, Theorem 1, Eq. (18)] The LMI in Theorem 1 misses the decay rate alpha in the (1,1) block. With P = S^{-1} = Z0 G1, the Schur complement of G1^T Z1^T P^{-1} Z1 G1 - alpha P <= 0 is [[alpha P, G1^T Z1^T], [Z1 G1, P]] >= 0, not [[Z0 G1, G1^T Z1^T], [Z1 G1, Z0 G1]] >= 0. As written, (18) only enforces a neutral (alpha = 1) decrease condition, and the derivation's step 'pre- and post-multiply by S^{-1}' is consistent with the corrected LMI rather than with the displayed matrix. The statement that the resulting K guarantees decay rate alpha is therefore unsupported.
  3. [Section 3.4, Theorem 2 and Eq. (21)] The S-procedure condition has the wrong sign. To deduce the Lyapunov decrease from the triggering condition v^T M v <= 0 with M = diag(-gamma^2 I, I), one requires an eta >= 0 such that Psi - eta M <= 0 (equivalently eta M - Psi >= 0). The proof writes eta M <= Psi, which is the reverse and cannot be used to conclude that (4) implies (16). The subsequent Schur-complement substitution then produces a different inequality, and it is unclear whether the LMI (21) is the correct condition. A corrected derivation is needed before the threshold gamma* can be trusted.
  4. [Sections 2.2 and 3.1] The control and triggering laws are specified inconsistently across coordinate systems. Eq. (2) gives u_k = K x_{k_i}, while the footnote and the rest of Section 3 use u_k = K xi(x_{k_i}); Eq. (4) uses ||e_k|| <= gamma ||x_k|| in original coordinates, but Eq. (11) switches to ||e_xi_k|| <= gamma ||xi(x_k)||, and the closed-loop analysis (13) reuses e_k without redefining it in the lifted space. If the implemented controller uses x_k, then Theorems 1 and 2 do not apply to the simulated system; if it uses xi(x_k), then Eq. (2) and the plots in Section 4 need to be updated. The paper should consistently analyze the lifted loop or the original loop and clearly state which one is implemented.
minor comments (6)
  1. [Section 2.2] The notation U(a,b) is said to represent a normal distribution, but the text and examples use it as a uniform distribution; please correct the definition.
  2. [Section 2.2 and Eq. (4)] The controller gain K is introduced as R^{m x n}, but after lifting it becomes m x p. Please adjust the dimension statements and ensure the error vector e_k is defined consistently in both original and lifted coordinates.
  3. [Section 3.4, proof of Theorem 2] In the S-procedure matrix, the off-diagonal blocks are written as L^T Z1^T S Z1 L in both positions; the second should read L^T Z1^T S Z1 N (and its transpose). This is likely a typo, but it obscures the derivation.
  4. [Section 4.2 and Fig. 7] The dictionary listing includes identical entries 'x3 1 x3 2 x3 1 x3 2', which seems to be a typo for distinct monomials; please clarify.
  5. [Section 4.1 and Eq. (25)] In Eq. (25) the third control term is written as K3 x2 2; based on the observable x_1^2 this should be K3 x_1^2. The same typo appears in Section 5.2.
  6. [Throughout] There are multiple typos, including 'Lyaponuv' instead of 'Lyapunov' and inconsistent capitalization of 'Koopman' in places. A careful proofreading pass is recommended.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the theorems are algebraic translations of Lyapunov conditions into data-dependent LMIs; the unverified dictionary closure is a soundness gap, not a circular step.

full rationale

The derivation chain is self-contained. Lemma 1 reparameterizes the lifted closed loop z_{k+1} = A z_k + B u_k via (14) into the data-driven form (15), z_{k+1} = Z1 L z_k + Z1 N e_k, using the identity [A B][Z0;U0] = Z1. Theorem 1 translates the Lyapunov decrease condition L^T Z1^T S Z1 L - alpha S <= 0 into LMI (18) via Schur complement and the variable changes G1 = L S^{-1}, S^{-1} = Z0 G1, yielding K = U0 G1 (Z0 G1)^{-1}; Theorem 2 does the same for the event-triggering threshold using the S-procedure, Schur complement, and the substitutions G2 = eta^{-1} N, q = eta^{-1}. These are algebraic equivalences, not fitted parameters renamed as predictions. The self-citations [11] and [31] appear only in the introductory survey as example applications and are not load-bearing. The event-triggering threshold gamma is computed to enforce V(z_{k+1}) <= alpha V(z_k) on the lifted data-driven loop, which is a standard design certificate rather than a circular prediction. The paper's genuine limitation is a soundness gap: Theorems 1 and 2 certify only the lifted data-driven system (15), while for a generic dictionary the closure residual R_k = Xi(x_{k+1}) - (Z1 L Xi(x_k) + Z1 N e_k) is nonzero, as Example 2 in Section 4.2 acknowledges via the closure problem. No approximation-error bound transfers the guarantee to the original nonlinear plant (1), but that is an unverified modeling assumption, not circularity.

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

The main unpaid-for ingredients are the hand-picked observable dictionary and the unquantified approximation error of the Koopman lifting. The LMI machinery itself is standard in the data-driven control literature, and the paper's assumptions are mostly standard persistency-of-excitation conditions. No new physical entities are introduced.

free parameters (3)
  • Decay rate alpha = 0.7 (Example 2), 0.9 (Example 3), swept over [0.4, 1] (Example 1)
    User-chosen convergence rate; enters both LMIs and directly trades off trigger frequency against stability margin.
  • Observable dictionary Xi = Example 1: [x1, x2, x1^2]; Example 2: ten monomials up to degree 3; Example 3: identity
    Hand-selected lifting functions; the paper shows the steady-state error depends strongly on this choice (Fig. 7) and that increasing polynomial degree can hurt (degree 6 overfit). The choice is not derived from data or theory.
  • Data horizon T and input signal = T=45, u~N(0,1) (Example 1); T=150, closed-loop with perturbing noise (Example 2); T=20, u random in [-3,3] (Example 3)
    Data collection is a design choice; Assumption 1 only requires T >= p+m and full row rank, which the simulations satisfy, but the specific signals affect the resulting K and gamma.
assumptions (4)
  • standard math Rouché-Capelli theorem guarantees existence of L and N satisfying (14) under Assumption 1
    Used in Lemma 1 proof to argue the data-driven closed-loop representation (15) with Z0 L = I_p is well-posed.
  • domain assumption The chosen observables Xi yield a finite-dimensional Koopman-invariant subspace so that (12) captures (1) exactly or with negligible error
    Invoked in Section 3.1 when asserting z_{k+1} = A z_k + B u_k; Example 2 shows the approximation is not exact, yet the stability proof does not account for the error.
  • domain assumption Persistency of excitation: the data matrix [Z0; U0] has full row rank (Assumption 1)
    Required for Lemma 1 and both theorems; the paper notes it can be verified numerically but does not check it explicitly for the examples.
  • standard math S-procedure equivalence for the triggering condition and Lyapunov inequality
    Used in Theorem 2 proof to convert the implication (4) => (16) into an LMI with a scalar multiplier eta.

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Cite this review

Pith. "Pith review of Koopman-Based Event-Triggered Control from Data." pith.science (2026). https://pith.science/paper/GB2RWBOF

@misc{pith2026250414334,
  author       = {Pith},
  title        = {Pith review of: Koopman-Based Event-Triggered Control from Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GB2RWBOF}},
  note         = {Machine review of arXiv:2504.14334}
}
read the original abstract

Event-triggered Control (ETC) presents a promising paradigm for efficient resource usage in networked and embedded control systems by reducing communication instances compared to traditional time-triggered strategies. This paper introduces a novel approach to ETC for discrete-time nonlinear systems using a data-driven framework. By leveraging Koopman operator theory, the nonlinear system dynamics are globally linearized (approximately in practical settings) in a higher-dimensional space. We design a state-feedback controller and an event-triggering policy directly from data, ensuring exponential stability in Lyapunov sense. The proposed method is validated through extensive simulation experiments, demonstrating significant resource savings.

Figures

Figures reproduced from arXiv: 2504.14334 by the authors.

Figure 2
Figure 2. Illustration of the Koopman Operator: The [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Results of the illustrative example 1. (a) Behaviour of state [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 5
Figure 5. The relationship between α and the Lyapunov func￾tion decay rate. Simulations confirm no violations in the decay rate, as all points lie below the boundary max V(k+1)/V(k)  = α, ensuring system stability across the tested α range. able functions. This means that we implicitly assume that the nonlinear system in (24) can be well represented using linear observables, which is not evident from the most left bar of [P… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: A simulation of ten random initial conditions drawn [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 6
Figure 6. Figure 6: Results of the illustrative example 2. (a) Behaviour of state [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: Steady-state error versus polynomial degree of the [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Results of the illustrative example 3. (a) Behaviour of state [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

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Reference graph

Works this paper leans on

60 extracted references · 56 canonical work pages

  1. [1]

    A simple event-based PID controller

    Karl-Erik Åarzén. A simple event-based PID controller. IFAC Proceedings Volumes, 32(2):8687–8692, 1999

    work page 1999

  2. [2]

    A feed- back scheduler for real-time controller tasks

    Johan Eker, Per Hagander, and Karl-Erik Årzén. A feed- back scheduler for real-time controller tasks. Control Engineering Practice, 8(12):1369–1378, 2000

    work page 2000

  3. [3]

    Event-triggered real-time scheduling of stabilizing control tasks

    Paulo Tabuada. Event-triggered real-time scheduling of stabilizing control tasks. IEEE Transactions on Automatic control, 52(9):1680–1685, 2007

    work page 2007

  4. [4]

    An introduction to event-triggered and self-triggered control

    Wilhelmus PMH Heemels, Karl Henrik Johansson, and Paulo Tabuada. An introduction to event-triggered and self-triggered control. In 2012 ieee 51st ieee conference Preprint – Koopman-Based Event-Triggered Control from Data 10 on decision and control (cdc), pages 3270–3285. IEEE, 2012

    work page 2012

  5. [5]

    Data-driven LQR control design

    Gustavo R Gonçalves da Silva, Alexandre S Bazanella, Charles Lorenzini, and Luciola Campestrini. Data-driven LQR control design. IEEE control systems letters, 3(1): 180–185, 2018

    work page 2018

  6. [6]

    Formulas for data- driven control: Stabilization, optimality, and robustness

    Claudio De Persis and Pietro Tesi. Formulas for data- driven control: Stabilization, optimality, and robustness. IEEE Transactions on Automatic Control, 65(3):909–924, 2019

    work page 2019

  7. [7]

    Enhancement for ro- bustness of koopman operator-based data-driven mobile robotic systems

    Lu Shi and Konstantinos Karydis. Enhancement for ro- bustness of koopman operator-based data-driven mobile robotic systems. In 2021 IEEE International Conference on Robotics and Automation (ICRA), pages 2503–2510. IEEE, 2021

    work page 2021

  8. [8]

    Quadrotor Trajectory Tracking with Learned Dynamics: Joint Koopman-based Learning of System Models and Function Dictionaries

    Carl Folkestad, Skylar X Wei, and Joel W Burdick. Quadrotor trajectory tracking with learned dynamics: Joint koopman-based learning of system models and func- tion dictionaries. arXiv preprint arXiv:2110.10341, 2021

    work page Pith review arXiv 2021

Show all 60 references
  1. [9]

    Applied koopman operator theory for power systems technology

    Yoshihiko Susuki, Igor Mezic, Fredrik Raak, and Takashi Hikihara. Applied koopman operator theory for power systems technology. Nonlinear Theory and Its Applica- tions, IEICE, 7(4):430–459, 2016

    2016

  2. [10]

    Discovering governing equations from data by sparse identification of nonlinear dynamical systems

    Steven L Brunton, Joshua L Proctor, and J Nathan Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceed- ings of the national academy of sciences, 113(15):3932– 3937, 2016

    2016

  3. [11]

    Data-driven discovery of the quadrotor equa- tions of motion via sparse identification of nonlinear dy- namics

    Zeyad M Manaa, Mohammed R Elbalshy, and Ayman M Abdallah. Data-driven discovery of the quadrotor equa- tions of motion via sparse identification of nonlinear dy- namics. In AIAA SCITECH 2024 Forum , page 1308, 2024

    2024

  4. [12]

    Modeling and prediction of the transmission dynamics of COVID-19 based on the SINDy- LM method

    Yu Xin Jiang, Xiong Xiong, Shuo Zhang, Jia Xiang Wang, Jia Chun Li, and Lin Du. Modeling and prediction of the transmission dynamics of COVID-19 based on the SINDy- LM method. Nonlinear Dynamics, 105:2775–2794, 2021. ISSN 1573269X. Number: 3

    2021

  5. [13]

    Sparse Identification for Nonlinear Optical Com- munication Systems: SINO Method

    Mariia Sorokina, Stylianos Sygletos, and Sergei Turit- syn. Sparse Identification for Nonlinear Optical Com- munication Systems: SINO Method. Opt. Express, 24 (26):30433, December 2016. ISSN 1094-4087. doi: 10.1364/OE.24.030433

    2016 doi

  6. [14]

    Operable adaptive sparse identification of systems: Application to chemical processes

    Bhavana Bhadriraju, Mohammed Saad Faizan Bangi, Ab- hinav Narasingam, and Joseph Sang Il Kwon. Operable adaptive sparse identification of systems: Application to chemical processes. AIChE Journal, 66(11), 2020. ISSN 15475905. doi: 10.1002 /aic.16980. Number: 11

    2020

  7. [15]

    Cheng, and Weiliang Xu

    Dipankar Bhattacharya, Leo K. Cheng, and Weiliang Xu. Sparse Machine Learning Discovery of Dynamic Differen- tial Equation of an Esophageal Swallowing Robot. IEEE Transactions on Industrial Electronics, 67(6):4711–4720,

  8. [16]

    Control oriented learning in the era of big data

    Mario Sznaier. Control oriented learning in the era of big data. IEEE Control Systems Letters, 5(6):1855–1867, 2020

    2020

  9. [17]

    Virtual reference feedback tuning: a direct method for the design of feedback controllers

    Marco C Campi, Andrea Lecchini, and Sergio M Savaresi. Virtual reference feedback tuning: a direct method for the design of feedback controllers. Automatica, 38(8): 1337–1346, 2002

    2002

  10. [18]

    Model-free control

    Michel Fliess and Cédric Join. Model-free control. Inter- national journal of control, 86(12):2228–2252, 2013

    2013

  11. [19]

    Data-driven self-triggered control via trajectory prediction

    Wenjie Liu, Jian Sun, Gang Wang, Francesco Bullo, and Jie Chen. Data-driven self-triggered control via trajectory prediction. IEEE Transactions on Automatic Control, 68 (11):6951–6958, 2023

    2023

  12. [20]

    Data- driven event-triggered control for discrete-time LTI sys- tems

    Vijayanand Digge and Ramkrishna Pasumarthy. Data- driven event-triggered control for discrete-time LTI sys- tems. In 2022 European Control Conference (ECC), pages 1355–1360. IEEE, 2022

    2022

  13. [21]

    Model-based and data-driven control of event-and self-triggered discrete-time linear systems

    Xin Wang, Julian Berberich, Jian Sun, Gang Wang, Frank Allgöwer, and Jie Chen. Model-based and data-driven control of event-and self-triggered discrete-time linear systems. IEEE Transactions on Cybernetics, 2023

    2023

  14. [22]

    Hamiltonian systems and trans- formation in hilbert space

    Bernard O Koopman. Hamiltonian systems and trans- formation in hilbert space. Proceedings of the National Academy of Sciences, 17(5):315–318, 1931

    1931

  15. [23]

    Dynamical sys- tems of continuous spectra

    Bernard O Koopman and J v Neumann. Dynamical sys- tems of continuous spectra. Proceedings of the National Academy of Sciences, 18(3):255–263, 1932

    1932

  16. [24]

    Comparison of sys- tems with complex behavior

    Igor Mezi´c and Andrzej Banaszuk. Comparison of sys- tems with complex behavior. Physica D: Nonlinear Phe- nomena, 197(1-2):101–133, 2004

    2004

  17. [25]

    Spectral properties of dynamical systems, model reduction and decompositions

    Igor Mezi´c. Spectral properties of dynamical systems, model reduction and decompositions. Nonlinear Dynam- ics, 41:309–325, 2005

    2005

  18. [26]

    Koopman-based control of a soft continuum manipulator under variable loading conditions

    Daniel Bruder, Xun Fu, R Brent Gillespie, C David Remy, and Ram Vasudevan. Koopman-based control of a soft continuum manipulator under variable loading conditions. IEEE robotics and automation letters, 6(4):6852–6859, 2021

    2021

  19. [27]

    Derivative-based koopman operators for real-time control of robotic systems

    Giorgos Mamakoukas, Maria L Castano, Xiaobo Tan, and Todd D Murphey. Derivative-based koopman operators for real-time control of robotic systems. IEEE Transac- tions on Robotics, 37(6):2173–2192, 2021

    2021

  20. [28]

    Koopman operator based model predictive control for tra- jectory tracking of an omnidirectional mobile manipulator

    Xuehong Zhu, Chengjun Ding, Lizhen Jia, and Yubo Feng. Koopman operator based model predictive control for tra- jectory tracking of an omnidirectional mobile manipulator. Measurement and Control, 55(9-10):1067–1077, 2022

    2022

  21. [29]

    Deep koop- man with control: Spectral analysis of soft robot dynam- ics

    Naoto Komeno, Brendan Michael, Katharina Küchler, Edgar Anarossi, and Takamitsu Matsubara. Deep koop- man with control: Spectral analysis of soft robot dynam- ics. In 2022 61st Annual Conference of the Society of Instrument and Control Engineers (SICE) , pages 333–

    2022

  22. [30]

    Desko: Stability-assured robust control Preprint – Koopman-Based Event-Triggered Control from Data 11 with a deep stochastic koopman operator

    Minghao Han, Jacob Euler-Rolle, and Robert K Katzschmann. Desko: Stability-assured robust control Preprint – Koopman-Based Event-Triggered Control from Data 11 with a deep stochastic koopman operator. InInternational Conference on Learning Representations, 2021

    2021

  23. [31]

    Koopman-LQR Con- troller for Quadrotor UA Vs from Data

    Zeyad M Manaa, Ayman M Abdallah, Mohammad A Abido, and Syed S Azhar Ali. Koopman-LQR Con- troller for Quadrotor UA Vs from Data. arXiv preprint arXiv:2406.17973, 2024

    2024 arXiv

  24. [32]

    Data-driven linear koopman embedding for net- worked systems: Model-predictive grid control

    Ramij Raja Hossain, Rahmat Adesunkanmi, and Ratnesh Kumar. Data-driven linear koopman embedding for net- worked systems: Model-predictive grid control. IEEE Systems Journal, 2023

    2023

  25. [33]

    Koopman-based surrogate modelling of tur- bulent rayleigh-b\’enard convection

    Thorben Markmann, Michiel Straat, and Barbara Ham- mer. Koopman-based surrogate modelling of tur- bulent rayleigh-b\’enard convection. arXiv preprint arXiv:2405.06425, 2024

    2024 arXiv

  26. [34]

    A koopman operator-based prediction algorithm and its application to covid-19 pandemic and influenza cases

    Igor Mezi ´c, Zlatko Drma ˇc, Nelida ˇCrnjari´c, Senka Ma´ceši´c, Maria Fonoberova, Ryan Mohr, Allan M Avila, Iva Manojlovi´c, and Aleksandr Andrejˇcuk. A koopman operator-based prediction algorithm and its application to covid-19 pandemic and influenza cases. Scientific repor...

    2024

  27. [35]

    A note on persistency of excitation

    Jan C Willems, Paolo Rapisarda, Ivan Markovsky, and Bart LM De Moor. A note on persistency of excitation. Systems & Control Letters, 54(4):325–329, 2005

    2005

  28. [36]

    Applied koopmanism

    Marko Budiši´c, Ryan Mohr, and Igor Mezi ´c. Applied koopmanism. Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(4), 2012

    2012

  29. [37]

    Koopman operator dynamical models: Learning, analysis and control

    Petar Bevanda, Stefan Sosnowski, and Sandra Hirche. Koopman operator dynamical models: Learning, analysis and control. Annual Reviews in Control , 52:197–212, 2021

    2021

  30. [38]

    Generalizing koopman theory to allow for inputs and control

    Joshua L Proctor, Steven L Brunton, and J Nathan Kutz. Generalizing koopman theory to allow for inputs and control. SIAM Journal on Applied Dynamical Systems , 17(1):909–930, 2018

    2018

  31. [39]

    Data-driven model predictive control using interpolated koopman generators

    Sebastian Peitz, Samuel E Otto, and Clarence W Rowley. Data-driven model predictive control using interpolated koopman generators. SIAM Journal on Applied Dynami- cal Systems, 19(3):2162–2193, 2020

    2020

  32. [40]

    Linear predictors for nonlin- ear dynamical systems: Koopman operator meets model predictive control

    Milan Korda and Igor Mezi´c. Linear predictors for nonlin- ear dynamical systems: Koopman operator meets model predictive control. Automatica, 93:149–160, 2018

    2018

  33. [41]

    Linearly recur- rent autoencoder networks for learning dynamics

    Samuel E Otto and Clarence W Rowley. Linearly recur- rent autoencoder networks for learning dynamics. SIAM Journal on Applied Dynamical Systems, 18(1):558–593, 2019

    2019

  34. [42]

    Learn- ing deep neural network representations for koopman operators of nonlinear dynamical systems

    Enoch Yeung, Soumya Kundu, and Nathan Hodas. Learn- ing deep neural network representations for koopman operators of nonlinear dynamical systems. In 2019 Amer- ican Control Conference (ACC), pages 4832–4839. IEEE, 2019

    2019

  35. [43]

    Deep learning for universal linear embeddings of nonlin- ear dynamics

    Bethany Lusch, J Nathan Kutz, and Steven L Brunton. Deep learning for universal linear embeddings of nonlin- ear dynamics. Nature communications, 9(1):4950, 2018

    2018

  36. [44]

    On analytical construction of observ- able functions in extended dynamic mode decomposition for nonlinear estimation and prediction

    Marcos Netto, Yoshihiko Susuki, Venkat Krishnan, and Yingchen Zhang. On analytical construction of observ- able functions in extended dynamic mode decomposition for nonlinear estimation and prediction. In 2021 Ameri- can Control Conference (ACC), pages 4190–4195. IEEE, 2021

    2021

  37. [45]

    Time-delay observables for koopman: Theory and applications

    Mason Kamb, Eurika Kaiser, Steven L Brunton, and J Nathan Kutz. Time-delay observables for koopman: Theory and applications. SIAM Journal on Applied Dy- namical Systems, 19(2):886–917, 2020

    2020

  38. [46]

    Local koopman operators for data-driven control of robotic systems

    Giorgos Mamakoukas, Maria Castano, Xiaobo Tan, and Todd Murphey. Local koopman operators for data-driven control of robotic systems. In Robotics: science and systems, 2019

    2019

  39. [47]

    Dynamic mode decomposition of numer- ical and experimental data

    Peter J Schmid. Dynamic mode decomposition of numer- ical and experimental data. Journal of fluid mechanics, 656:5–28, 2010

    2010

  40. [48]

    Dynamic mode decomposition with control

    Joshua L Proctor, Steven L Brunton, and J Nathan Kutz. Dynamic mode decomposition with control. SIAM Jour- nal on Applied Dynamical Systems, 15(1):142–161, 2016

    2016

  41. [49]

    Event-triggered control from data

    Claudio De Persis, Romain Postoyan, and Pietro Tesi. Event-triggered control from data. IEEE Transactions on Automatic Control, 2023

    2023

  42. [50]

    Convex opti- mization

    Stephen P Boyd and Lieven Vandenberghe. Convex opti- mization. Cambridge university press, 2004

    2004

  43. [51]

    Koopman invariant subspaces and fi- nite linear representations of nonlinear dynamical systems for control

    Steven L Brunton, Bingni W Brunton, Joshua L Proctor, and J Nathan Kutz. Koopman invariant subspaces and fi- nite linear representations of nonlinear dynamical systems for control. PloS one, 11(2), 2016

    2016

  44. [52]

    Linear observer synthesis for nonlinear systems using koopman operator framework

    Amit Surana and Andrzej Banaszuk. Linear observer synthesis for nonlinear systems using koopman operator framework. IFAC-PapersOnLine, 49(18):716–723, 2016

    2016

  45. [53]

    Koopman operator based observer synthesis for control-affine nonlinear systems

    Amit Surana. Koopman operator based observer synthesis for control-affine nonlinear systems. In 2016 IEEE 55th Conference on Decision and Control, pages 6492–6499. IEEE, 2016

    2016

  46. [54]

    Practical guidelines for data-driven identification of lifted linear predictors for control

    Loi Do, Adam Uchytil, and Zden ˇek Hurák. Practical guidelines for data-driven identification of lifted linear predictors for control. arXiv preprint arXiv:2408.01116, 2024

    2024 arXiv

  47. [55]

    A data–driven approximation of the koopman operator: Extending dynamic mode decom- position

    Matthew O Williams, Ioannis G Kevrekidis, and Clarence W Rowley. A data–driven approximation of the koopman operator: Extending dynamic mode decom- position. Journal of Nonlinear Science, 25:1307–1346, 2015

    2015

  48. [56]

    Deep learning- based construction of koopman observable functions for power system nonlinear dynamics

    Jiacheng Ge, Yijun Xu, and Zaijun Wu. Deep learning- based construction of koopman observable functions for power system nonlinear dynamics. In 2024 IEEE Power & Energy Society General Meeting (PESGM), pages 1–5. IEEE, 2024

    2024

  49. [57]

    Acd-edmd: Analyt- ical construction for dictionaries of lifting functions in koopman operator-based nonlinear robotic systems

    Lu Shi and Konstantinos Karydis. Acd-edmd: Analyt- ical construction for dictionaries of lifting functions in koopman operator-based nonlinear robotic systems. IEEE Robotics and Automation Letters, 7(2):906–913, 2021. Preprint – Koopman-Based Event-Triggered Control from Data 12

    2021

  50. [58]

    A kernel-based approach to data-driven koop- man spectral analysis

    Matthew O Williams, Clarence W Rowley, and Ioannis G Kevrekidis. A kernel-based approach to data-driven koop- man spectral analysis. arXiv preprint arXiv:1411.2260, 2014

    2014 arXiv

  51. [59]

    Kernel methods for the approximation of the eigenfunctions of the koopman operator

    Jonghyeon Lee, Boumediene Hamzi, Boya Hou, Houman Owhadi, Gabriele Santin, and Umesh Vaidya. Kernel methods for the approximation of the eigenfunctions of the koopman operator. arXiv preprint arXiv:2412.16588, 2024

    2024 arXiv

  52. [2020]

    doi: 10.1109 /TIE.2019.2928239

    ISSN 15579948. doi: 10.1109 /TIE.2019.2928239. Number: 6

    2019

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.