Pith. sign in

REVIEW 4 major objections 5 minor 34 references

Data-driven nonlinear output regulation via data-enforced incremental passivity

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Nonlinear output regulation can be solved from offline data: the paper proves that a data-driven passivating gain plus an internal model built from the known exosystem keeps all closed-loop trajectories bounded and drives the regulation…

desk verdict Solid data-driven passivation LMIs with a decoupled internal model, but Theorem 2's convergence proof assumes a steady-state trajectory that Assumption 2 does not guarantee; fixable and worth refereeing. read the letter →

arxiv 2506.06079 v2 pith:OZGUIAQU submitted 2025-06-06 eess.SY cs.SY

Yixuan Liu , Meichen Guo This is my paper · ORCID
classification eess.SYcs.SY MSC 93B5293C1093D1593D30
keywords data-drivencontroloutputregulationnonlinearsystemsincrementalpassivitypassivity-basedlinearmatrixinequalitiesinternalmodeltrajectorytracking
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 claims that for a class of nonlinear systems with unknown coefficient matrices, the output-regulation problem—asymptotic reference tracking and disturbance rejection—can be solved from a finite set of offline data plus knowledge of the exosystem that generates references and disturbances. The regulator combines a static data-driven feedback gain, characterized by linear matrix inequalities on the measured data that enforce incremental passivity, with an internal model constructed directly from the known exosystem. The paper's central result is that whenever the data-dependent LMIs are feasible and the standard regulator-equations assumptions hold, all closed-loop solutions stay bounded and the regulation error converges to zero. The same machinery also stabilizes a non-zero equilibrium when the equilibrium input is unknown. This matters because it offers a model-free route to asymptotic tracking in which the passivation step and the internal-model step are decoupled.

What carries the argument

The load-bearing mechanism is the data-based closed-loop representation combined with incremental passivity as the design target. From the offline samples one builds $X_0,Z_0,X_1,U_0,E_0$ and the exosystem-derived matrix $M_0$; any $G=(G_1,G_2)$ satisfying (17) produces data-based matrices $A_d=X_1G_1$, $B_d=X_1G_2$, $C_d=E_0G_1$ that agree with the true closed loop on the data. The passivity conditions of Lemma 3---$I^\top P(A+BK)+(\cdot)^\top \preceq 0$ and $I^\top PB=C^\top$---are then rewritten as LMIs (20) in variables $Y$, $G_2$, and a block-diagonal $P=\mathrm{blockdiag}(P_1,P_2)$, with storage function $V(x_1,x_2)=\frac12(x_1-x_2)^\top P_1^{-1}(x_1-x_2)$. The gain $K=U_0YP^{-1}$ is fixed by data alone, while the internal model $\dot\eta=S\eta-\alpha\Xi e$ is chosen from the known exosystem, so the two designs are independent; the interconnection lemma for incrementally passive systems supplies the augmented storage function that makes the convergence argument work.

What would settle it

Find a plant that satisfies Assumption 2 (so $x_{\mathrm{ss}}(w)$ and $u_{\mathrm{ss}}(w)$ are polynomials in $w$) but whose feature-map evaluation $Z(x_{\mathrm{ss}})$ contains frequencies outside the exosystem spectrum, and check numerically whether a bounded $\eta_{\mathrm{ss}}$ with $\dot\eta_{\mathrm{ss}}=S\eta_{\mathrm{ss}}$ and $\Xi^\top\eta_{\mathrm{ss}}=u_{\mathrm{ss}}-KZ(x_{\mathrm{ss}})$ exists for the passivating gain $K$ produced by the LMIs; if no such $\eta_{\mathrm{ss}}$ exists, the comparison trajectory used in the proof is unavailable and the theorem's conclusion does not follow for that allowed instance.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that incremental passivity can be enforced directly from data and then used as the organizing principle for output regulation. The plant is written as $\dot x = A Z(x) + B u + E w$, $e = C Z(x) + F w$ with unknown $A,B,C,E,F$ and a known feature map $Z(x)$; Lemma 5 shows that the closed-loop matrices $A+BK$, $B$, $C$ can be represented by the data matrices $X_1 G_1$, $X_1 G_2$, $E_0 G_1$ whenever the compatibility equation (17) is solvable. This turns the model-based passivation conditions of Lemma 3 into the data-dependent LMIs (20), whose feasibility is the design certificate. Theorem 2 then states that with those LMIs feasible, the regulator $\dot\eta = S\eta - \alpha\Xi e$, $u = KZ(x) + \Xi^\top\eta - \hat K e$ renders the augmented system incrementally passive with respect to a steady-state comparison trajectory, and Barbalat's lemma converts the resulting dissipation inequality into $\lim_{t\to\infty} e(t)=0$ with bounded closed-loop trajectories. The method also yields, via a virtual output $e_v = \|x-x_e\|^2$, global asymptotic stabilization at a non-zero equilibrium without estimating the equilibrium input.

Load-bearing premise

The load-bearing premise is that the internal model can reproduce the steady-state part of the control input---the proof needs a bounded $\eta_{\mathrm{ss}}$ following $\dot\eta=S\eta$ with $\Xi^\top\eta_{\mathrm{ss}}=u_{\mathrm{ss}}-KZ(x_{\mathrm{ss}})$---while Assumption 2 only guarantees a plant-level steady state $(x_{\mathrm{ss}},u_{\mathrm{ss}})$ exists, and the paper gives no rule for choosing $\Xi$ to make the matching possible.

Editorial extensions

If this is right

  • If Theorem 2 is right, asymptotic tracking and disturbance rejection for this class of nonlinear systems need no identification of $A,B,C,E,F$: feasibility of the data-dependent LMIs (20) is a direct design certificate.
  • Because the passivating gain is independent of the internal model, changing the reference or disturbance spectrum only requires replacing the internal model (and recollecting data to reflect the new exosystem), not redesigning the passivation controller.
  • The same data-driven passivation, with the virtual output $e_v=\|x-x_e\|^2$, yields global asymptotic stabilization at a non-zero equilibrium without knowing or estimating the equilibrium input, while rejecting time-varying disturbances.
  • For linear plants ($Z(x)=x$), the result reduces to Corollary 1, a data-driven linear output regulator with the same passivity-based proof structure.
  • The design goes beyond earlier data-driven nonlinear regulation of periodic references, which gave bounded tracking error, to asymptotic error convergence for step-plus-sinusoidal exosystems.

Reading between the lines

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

  • Beyond the paper: the decoupling of passivation from the internal model suggests a modular control architecture in which a single data-driven passivating gain is precomputed per plant and stored, and only the internal model is swapped when the reference or disturbance task changes.
  • Beyond the paper: the proof's comparison trajectory requires the internal model to generate the steady-state input, a condition beyond Assumption 2; a practical safeguard is to check whether $\Xi^\top\eta_{\mathrm{ss}}=u_{\mathrm{ss}}-KZ(x_{\mathrm{ss}})$ is solvable for a bounded $\eta_{\mathrm{ss}}$, or to enlarge the internal model with additional harmonics when $Z(x_{\mathrm{ss}})$ contains fr
  • Beyond the paper: the virtual-output reformulation suggests the same machinery can handle objectives beyond equilibria---any regulation task expressible as a known polynomial error $e_v=C_vZ_v(x)+F_vw_v$ could be attacked with the same data-driven passivation.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper proposes a data-driven output regulation scheme for a class of nonlinear systems with unknown matrices A, B, C, E, F, where the reference and disturbances are generated by a known linear exosystem. The controller consists of a static nonlinear feedback u = K Z(x) + Ξ^T η − K̂ e and a linear internal model η̇ = Sη − αΞ e. The gain K is obtained from offline data via LMIs that enforce incremental passivity of the closed-loop system with respect to the regulation error and a virtual input. The main theorem (Theorem 2) claims that if these data-dependent LMIs are feasible, then the regulator asymptotically drives the error to zero. A stabilization extension for non-zero equilibria with unknown equilibrium input is also given, along with three numerical examples.

Significance. If the main theorem were correct, the paper would offer a clean, decoupled, data-driven design for nonlinear output regulation with asymptotic guarantees, building on the model-based incremental passivity framework of Pavlov and Marconi and the data-based contraction conditions of Hu et al. The LMI conditions are derived from first principles, the data representation (17) is clearly explained, and the numerical examples are reproducible in structure. However, the central convergence proof contains an unproved existence assertion for a zero-error steady state of the augmented system, and the internal model's incremental passivity is only established for a restricted class of exosystem matrices. These gaps currently prevent the main theorem from being accepted as stated.

major comments (4)
  1. [Section 4, Theorem 2] The proof of Theorem 2 asserts, without proof, that 'Under Assumption 2, system (24) admits a bounded solution ζss(t) = (x(w), ηss(t))'. Assumption 2 only guarantees a plant-level solution (x(w), u(w)) of the regulator equations (5). For the augmented system to have a zero-error bounded solution, there must exist ηss(t) such that η̇ss = S ηss and Ξ^T ηss(t) = u(w(t)) − K Z(x(w(t))). No condition on Ξ is stated in Theorem 2 and no design rule is given, so the comparison trajectory used in the incremental passivity inequality and in the Barbalat argument may not exist. This is load-bearing: the entire convergence proof relies on this trajectory. For polynomial x(w), u(w), the right-hand side generically contains harmonics that an internal model with only exosystem frequencies cannot produce. Example 1 does not rescue the theorem as stated, because although the specific K = [-0.1290 -0.0132 1.0000] cancels the sin(sin 2t) term in the steady-state residual, the theorem does not require or prove such cancellation.
  2. [Section 4, internal model (21), Lemma 1] The storage function V_IM = (1/(2α))||η1−η2||^2 yields a derivative with the term (1/α)(η1−η2)^T S(η1−η2), which must be nonpositive for the internal model to be incrementally passive. This holds only if S + S^T ⪯ 0, which for matrices with all eigenvalues on the imaginary axis is equivalent to S being skew-symmetric. Assumption 1 (all eigenvalues of S have zero real part) does not imply skew-symmetry; for example, S = [[0,2],[-0.5,0]] has eigenvalues ±i and S+S^T is indefinite. Thus the application of Lemma 1 to the internal model is unjustified for exosystems satisfying only Assumption 1. The authors should either assume S is skew-symmetric (or S+S^T ⪯ 0) or use a weighted storage function with a positive definite solution to the Lyapunov equation S^T P + P S = 0.
  3. [Section 2, equations (4)-(6), Remark 1] The representation W0 = Γ M0 with M(t) = [M1(t)^T ... 1_{q2}^T]^T is valid only for exosystem matrices that are block diagonal with 2x2 rotation blocks and a zero block, i.e., S is semi-simple with purely imaginary eigenvalues. Assumption 1 only states that all eigenvalues have zero real part, which permits nontrivial Jordan blocks (e.g., a double integrator S = [[0,1],[0,0]]). For such S, M0 does not capture polynomial-in-time signals, and the derivation X1 = A Z0 + B U0 + E W0 with W0 = Γ M0 in Lemma 5 fails. The theorem's assumptions therefore do not match the data representation used in the proofs of Theorems 1 and 2. The authors should either restrict Assumption 1 to semi-simple S or extend the data representation to handle Jordan blocks.
  4. [Section 4, Example 1, Assumption 2] Assumption 2 requires x(w) and u(w) to be polynomials in w. For the pendulum example, the steady-state input obtained from the regulator equations is u(w) = 0.1(−3w1 + √3 w2) + sin(w1) + 0.1(1.5w2 + √3/2 w1) − 0.1, which contains sin(w1) and is not a polynomial in w. Thus Example 1 does not satisfy Assumption 2 and is not covered by Theorem 2. If the authors intend to allow non-polynomial steady-state solutions, Assumption 2 should be reformulated and the existence claim in Theorem 2 should be proved under the weaker assumption.
minor comments (5)
  1. [Section 4, equation (23)] The interconnection should read '˜e = −e + v̂IM' rather than 'e = −e + v̂IM'.
  2. [Section 4, proof of Theorem 2] The statement 'Vaug_dot < 0 when ζ(t) ≠ ζss(t)' is not implied by the derived inequality Vaug_dot ≤ −e^T K̂ e ≤ 0, since e can vanish while ζ differs from ζss. This overstatement is not needed for the Barbalat argument.
  3. [Section 3, Lemma 3 and Theorem 1] The matrix I is defined as [I_n 0_{n×(nZ−n)}] in Lemma 3, but later used in I^T X1 Y in Theorem 1 without a reminder of its dimensions; a brief restatement would improve readability.
  4. [Remark 1] The claim that Assumption 1 is 'slightly less restrictive than the one posed in [17]' is not substantiated; if the comparison concerns the eigenstructure used in the data representation, the statement should be qualified.
  5. [Figures 2-4] The figure captions do not list the controller parameters (α, K̂, Ξ) used in the simulations; including these values would aid reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the data-driven LMI passivation and regulator synthesis are derived from stated assumptions; the missing proof of the internal-model steady state in Theorem 2 is a correctness gap, not a circular reduction.

full rationale

The paper's derivation is not circular. Theorem 1 obtains the data-based closed-loop representation via Lemma 5 and then characterizes passivation by the feasibility LMIs (20); the decision variables Y, G2, P define K = U0 Y P^-1, so K is a feasibility output, not a fitted constant. The passivity proof follows the same calculation as Lemma 3 and does not use the tracking objective as an input. Theorem 2 interconnects this incrementally passive closed-loop system with the internal model (21), whose dynamics use only the known exosystem matrix S and the arbitrary matrices alpha, Xi, and Ktilde. The convergence step uses the regular storage function (25), the dissipation inequality with the negative feedback Ktilde, and Barbalat's lemma; this is a standard consequence of incremental passivity and does not reuse the data as a fitted prediction. There is no load-bearing self-citation chain: [6] is an external 2008 incremental-passivity result, [16] is used only for the data-representation idea, and [34] is cited only as related prior work. The one substantive weakness is a non-circular proof gap: the statement 'Under Assumption 2, system (24) admits a bounded solution zeta_ss(t) = (x(w), eta_ss(t))' assumes, without proof or any condition on Xi, that the internal model can generate the steady-state residual u(w) - KZ(x(w)) via eta_dot = S eta and Xi^T eta_ss = u(w) - KZ(x(w)). Assumption 2 alone guarantees only the plant-level regulator equations (5), and Example 1 illustrates that the residual can contain components not in the S-invariant signal space unless the passivating gain cancels them. This is a legitimate correctness concern that should be addressed by adding a matching condition on Xi or by explicitly constructing eta_ss, but it is not a reduction of the claimed result to its own inputs; the LMI conditions and the internal-model interconnection remain independent of the convergence conclusion.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. It relies on standard output regulation assumptions plus an unproved existence claim about the steady state of the augmented system; that existence claim is the most fragile item in the ledger.

free parameters (1)
  • Internal model output matrix Ξ = [1 0 1]^T (Examples 1-2), [1 1 1]^T (Example 3)
    Chosen by hand in every example. The theorem states no condition on Ξ, yet the proof requires the internal model to generate the steady-state control component. The paper gives no design rule, so Ξ is a free parameter affecting the central guarantee.
assumptions (5)
  • domain assumption Assumption 1: all eigenvalues of S have zero real part
    Section 2, used to write exosystem data as W0 = Γ M0 with known M0, and for the internal model to generate bounded steady-state signals.
  • domain assumption Assumption 2: there exist polynomial x(w), u(w) solving the regulator equations (5)
    Section 2, Eq. (5); invoked in Theorem 2 to assert existence of the steady-state solution ζss(t). The paper states in Remark 1 that verifying (5) from data is out of scope.
  • ad hoc to paper Existence of bounded ζss(t) with e=0 for the augmented system (24) for the chosen Ξ
    Theorem 2 proof asserts this without proof. It is not implied by Assumption 2 alone and depends on the unstated relationship between Ξ and the steady-state input.
  • domain assumption Noiseless data and known library Z(x)
    Remark 5 excludes measurement noise; Lemma 5 requires exact identity X1 = A Z0 + B U0 + E Γ M0. Z(x) must be known to construct matrices and the controller.
  • domain assumption Rank and excitation condition: [Z0; U0] (and related stacked matrices) full row rank
    Remark 5 requires T ≥ nZ + m and persistent excitation for (17) and (20) to be solvable. No further feasibility analysis is given.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Data-driven nonlinear output regulation via data-enforced incremental passivity." pith.science (2026). https://pith.science/paper/OZGUIAQU

@misc{pith2026250606079,
  author       = {Pith},
  title        = {Pith review of: Data-driven nonlinear output regulation via data-enforced incremental passivity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OZGUIAQU}},
  note         = {Machine review of arXiv:2506.06079}
}
read the original abstract

This work proposes a data-driven nonlinear regulator design that achieves asymptotic reference tracking under external disturbances, where the reference and disturbances are generated by a linear exosystem. The key idea is to design a data-driven feedback controller such that the closed-loop system is incrementally passive with respect to the regulation error and a virtual input. By interconnecting the closed-loop system with an internal model and carefully designing the virtual input, we solve the data-driven nonlinear output regulation problem. We characterize the passivation feedback controller by a set of data-dependent linear matrix inequalities, which is independent of the internal model. This decoupled design offers high data efficiency and design flexibility. The proposed approach also solves the non-zero equilibrium stabilization problem of a class of nonlinear systems with unknown equilibrium input. Numerical examples are presented to illustrate the effectiveness of the proposed designs.

Figures

Figures reproduced from arXiv: 2506.06079 by the authors.

Figure 1
Figure 1. Interconnection of the closed-loop system and the internal [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Regulation error of the simple pendulum with various ini [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 4
Figure 4. 0 20 40 60 80 100 120 140 160 180 200 -2 -1.5 -1 -0.5 0 0 20 40 60 80 100 120 140 160 180 200 -2 -1.5 -1 -0.5 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

34 extracted references · 32 canonical work pages

  1. [17]

    Data-driven harmonic output regulation of a class of nonlinear systems,

    Z. Hu, C. De Persis, J. W. Simpson-Porco, and P. Tesi, “Data-driven harmonic output regulation of a class of nonlinear systems,”Systems & Control Let- ters, vol. 200, 2025

    work page 2025

  2. [16]

    Enforcing contraction via data

    Z. Hu, C. De Persis, and P. Tesi, “Enforcing con- traction via data,”arXiv preprint arXiv:2401.07819, 2024

    work page Pith review arXiv 2024

  3. [1]

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

    C. De Persis and P. Tesi, “Formulas for data-driven control: Stabilization, optimality, and robustness,” IEEE Transactions on Automatic Control, vol. 65, no. 3, pp. 909–924, 2020

    work page 2020

  4. [2]

    Data informativity: A new per- spective on data-driven analysis and control,

    H. J. van Waarde, J. Eising, H. L. Trentelman, and M. K. Camlibel, “Data informativity: A new per- spective on data-driven analysis and control,”IEEE Transactions on Automatic Control, vol. 65, no. 11, pp. 4753–4767, 2020

    work page 2020

  5. [3]

    Data-driven stabilization of nonlinear polynomial systems with noisy data,

    M. Guo, C. De Persis, and P. Tesi, “Data-driven stabilization of nonlinear polynomial systems with noisy data,”IEEE Transactions on Automatic Con- trol, vol. 67, no. 8, pp. 4210 – 4217, 2022

    work page 2022

  6. [4]

    Direct data-driven state-feedback control of general nonlinear systems,

    C. Verhoek, P. J. W. Koelewijn, S. Haesaert, and R. Tóth, “Direct data-driven state-feedback control of general nonlinear systems,” inProceedings of the 62nd IEEE Conference on Decision and Control (CDC), Marina Bay Sands, Singapore, Dec. 2023, pp. 3688– 3693

    work page 2023

  7. [5]

    Guaran- tees for data-driven control of nonlinear systems us- ing semidefinite programming: A survey,

    T. Martin, T. B. Schön, and F. Allgöwer, “Guaran- tees for data-driven control of nonlinear systems us- ing semidefinite programming: A survey,”Annual Re- views in Control, vol. 56, p. 100911, 2023

    work page 2023

  8. [6]

    Incremental passivity and output regulation,

    A. Pavlov and L. Marconi, “Incremental passivity and output regulation,”Systems & Control Letters, vol. 57, pp. 400–409, 2008

    work page 2008

Show all 34 references
  1. [7]

    The internal model principleofcontroltheory,

    B. Francis and W. Wonham, “The internal model principleofcontroltheory,”Automatica, vol.12, no.5, pp. 457–465, 1976

    1976

  2. [8]

    The robust control of a servomecha- nism problem for linear time-invariant multivariable systems,

    E. Davison, “The robust control of a servomecha- nism problem for linear time-invariant multivariable systems,”IEEE Transactions on Automatic Control, vol. 21, no. 1, pp. 25–34, 1976

    1976

  3. [9]

    Output regulation of nonlinear systems,

    A. Isidori and C. I. Byrnes, “Output regulation of nonlinear systems,”IEEE Transactions on Automatic Control, vol. 35, no. 2, pp. 131–140, 1990. 11

    1990

  4. [10]

    Huang,Nonlinear Output Regulation

    J. Huang,Nonlinear Output Regulation. Society for Industrial and Applied Mathematics, 2004

    2004

  5. [11]

    Learning-based adaptive optimal tracking control of strict-feedback nonlinear systems,

    W. Gao and Z.-P. Jiang, “Learning-based adaptive optimal tracking control of strict-feedback nonlinear systems,”IEEE transactions on neural networks and learning systems, vol. 29, no. 6, pp. 2614–2624, 2017

    2017

  6. [12]

    Neural-network-based ap- proximate output regulation of discrete-time nonlin- ear systems,

    W. Lan and J. Huang, “Neural-network-based ap- proximate output regulation of discrete-time nonlin- ear systems,”IEEE transactions on neural networks, vol. 18, no. 4, pp. 1196–1208, 2007

    2007

  7. [13]

    Optimal output regulation of linear discrete-time systems with unknown dynamics using reinforcement learning,

    Y. Jiang, B. Kiumarsi, J. Fan, T. Chai, J. Li, and F. L. Lewis, “Optimal output regulation of linear discrete-time systems with unknown dynamics using reinforcement learning,”IEEE transactions on cyber- netics, vol. 50, no. 7, pp. 3147–3156, 2019

    2019

  8. [14]

    An informativity approach to the data-driven algebraic regulator problem,

    H. L. Trentelman, H. J. van Waarde, and M. K. Cam- libel, “An informativity approach to the data-driven algebraic regulator problem,”IEEE Transactions on Automatic Control, vol. 67, no. 11, pp. 6227–6233, 2022

    2022

  9. [15]

    Data informativity for robust output regulation,

    L. Zhu and Z. Chen, “Data informativity for robust output regulation,”IEEE Transactions on Automatic Control, 2024, doi 10.1109/TAC.2024.3389742

    2024

  10. [18]

    Data-driven robust output regulation of continuous-time LTI systems using Koopman op- erators,

    J. Deutscher, “Data-driven robust output regulation of continuous-time LTI systems using Koopman op- erators,”IEEE Transactions on Automatic Control, 2024, doi: 10.1109/TAC.2024.3414708

    2024

  11. [19]

    Provably robust verification of dissipativity properties from data,

    A. Koch, J. Berberich, and F. Allgöwer, “Provably robust verification of dissipativity properties from data,”IEEE Transactions on Automatic Control, vol. 67, no. 8, pp. 4248–4255, 2022

    2022

  12. [20]

    Data-driven system anal- ysis of nonlinear systems using polynomial approxi- mation,

    T. Martin and F. Allgöwer, “Data-driven system anal- ysis of nonlinear systems using polynomial approxi- mation,”IEEE Transactions on Automatic Control, vol. 69, no. 7, pp. 4261–4274, 2024

    2024

  13. [21]

    Data-driven dissipativity analysis of linear parameter-varying systems,

    C. Verhoek, J. Berberich, S. Haesaert, F. Allgöwer, and R. Tóth, “Data-driven dissipativity analysis of linear parameter-varying systems,”IEEE Transac- tions on Automatic Control, vol. 69, no. 12, pp. 8603– 8616, 2024

    2024

  14. [22]

    Passiv- ity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems,

    C. I. Byrnes, A. Isidori, J. C. Willemset al., “Passiv- ity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems,”IEEE Trans- actions on Automatic Control, vol. 36, no. 11, pp. 1228–1240, 1991

    1991

  15. [23]

    Adaptive passification of nonlinear systems,

    M. M. Seron, D. J. Hill, and A. L. Fradkov, “Adaptive passification of nonlinear systems,” inProceedings of 1994 33rd IEEE Conference on Decision and Control, vol. 1. IEEE, 1994, pp. 190–195

    1994

  16. [24]

    A passifi- cation approach to adaptive nonlinear stabilization,

    Z.-P. Jiang, D. J. Hill, and A. L. Fradkov, “A passifi- cation approach to adaptive nonlinear stabilization,” Systems & Control Letters, vol. 28, no. 2, pp. 73–84, 1996

    1996

  17. [25]

    On passivation with dynamic output feedback,

    M. Larsen and P. V. Kokotovic, “On passivation with dynamic output feedback,”IEEE transactions on Au- tomatic Control, vol. 46, no. 6, pp. 962–967, 2001

    2001

  18. [26]

    Passification-based adaptive control of linear sys- tems: Robustness issues,

    D. Peaucelle, A. Fradkov, and B. Andrievsky, “Passification-based adaptive control of linear sys- tems: Robustness issues,”International Journal of Adaptive Control and Signal Processing, vol. 22, no. 6, pp. 590–608, 2008

    2008

  19. [27]

    Passivity analysis and passification for uncertain signal processing systems,

    L. Xie, M. Fu, and H. Li, “Passivity analysis and passification for uncertain signal processing systems,” IEEE Transactions on Signal Processing, vol. 46, no. 9, pp. 2394–2403, 1998

    1998

  20. [28]

    H. K. Khalil,Nonlinear Systems, 3rd ed. Prentice Hall, 2002

    2002

  21. [29]

    YALMIP : A toolbox for modeling and optimization in MATLAB,

    J. Löfberg, “YALMIP : A toolbox for modeling and optimization in MATLAB,” inProceedings of the CACSD Conference, 2004

    2004

  22. [30]

    The MOSEK optimization toolbox for MATLAB manual, release 10.0.47,

    MOSEK ApS, “The MOSEK optimization toolbox for MATLAB manual, release 10.0.47,” 2023

    2023

  23. [31]

    R. M. Schmidt, G. Schitter, and A. Rankers,The Design of High Performance Mechatronics: High- Tech Functionality by Multidisciplinary System Inte- gration. Ios Press, 2020

    2020

  24. [32]

    Over- actuation for active damping in compliant position- ing stage using piezoelectric transducers,

    A. Natu, M. Kaczmarek, and S. HosseinNia, “Over- actuation for active damping in compliant position- ing stage using piezoelectric transducers,”IF AC- PapersOnLine, vol. 58, no. 7, pp. 269–274, 2024

    2024

  25. [33]

    Setpoint control of bilinear systems from noisy data,

    A. Bisoffi, D. M. Steeman, and C. De Persis, “Setpoint control of bilinear systems from noisy data,”arXiv preprint arXiv:2404.03594, 2024

    2024 arXiv

  26. [34]

    Data-driven stabilization of non-zero equilibrium for polynomial systems,

    Y. Liu and M. Guo, “Data-driven stabilization of non-zero equilibrium for polynomial systems,” in 2024 63rd IEEE Conference on Decision and Control (CDC), 2024, pp. 1128–1133. 12

    2024

Pith tools

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