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Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approach

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Pith's one-line read A distributed controller class based on port-Hamiltonian dynamics is claimed to guarantee finite L2 and incremental L2 gains for every neural-network parameter value, making stability-preserving control an unconstrained optimization…

desk verdict Sound L2-gain parametrization, but the incremental-L2 Theorem 4 is not proven: the proof drops the metric-derivative term and the claimed all-parameter iL2 guarantee fails on a simple example. read the letter →

arxiv 2411.10096 v2 pith:N7YCCF3K submitted 2024-11-15 eess.SY cs.LGcs.SY

Muhammad Zakwan , Giancarlo Ferrari-Trecate This is my paper · ORCID
classification eess.SYcs.LGcs.SY MSC 93C1093A1493D25
keywords port-HamiltoniansystemsdistributedcontrolL2gainincrementalstabilityunconstrainedparametrizationneuralnetworkcontrollersdiscretegradientmethods
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 tries to establish that a distributed controller built from port-Hamiltonian dynamics can carry arbitrary neural-network parameters and still be stable by design, in the input-output sense. The main results are an L2-gain theorem and an incremental L2-gain theorem: with the damping coefficient set to a fixed function of the controller's input matrix, every choice of parameters produces a controller with a prescribed gain bound, so no projection or constraint is needed during training. A dissipation-preserving discretization theorem says the same passivity property survives time discretization when a discrete-gradient integrator is used. If these results hold, gradient-based training of distributed nonlinear controllers, with communication sparsity built into the matrices, becomes a standard unconstrained optimization problem, and the same parametrization could serve as a stable-by-design model class for identification.

What carries the argument

The load-bearing object is the port-Hamiltonian controller $$\dot\xi = [J_c - (\$\alpha$ I + \Lambda)]\,\nabla H_c(\xi) + G_c y, \quad u = G_c^\top \nabla H_c(\xi),$$ where $J_c$ is a block-diagonal skew-symmetric interconnection matrix, $\Lambda$ is a diagonal nonnegative damping matrix, $G_c$ carries the communication graph's sparsity pattern, and $H_c$ is a differentiable, radially unbounded energy (Hamiltonian) function that can be a neural network. Port-Hamiltonian means the drift splits into a lossless skew-symmetric part and a dissipative damping part, which forces energy to decrease along trajectories. The proof mechanism is the same in each theorem: use the energy $H_c$ (or its curvature $\nabla^2 H_c$) as the storage function, then choose $\alpha \geq \epsilon\bar{\lambda}(G_cG_c^\top)$ so that the cross term involving $G_c$ is dominated and the required supply-rate inequality holds for every parameter value. This cancellation is what creates the unconstrained parametrization.

What would settle it

Compute the variational energy $V_\delta(\xi,\delta\xi)=\tfrac12\delta\xi^\top\nabla^2 H_c(\xi)\delta\xi$ for $H_c(\xi)=0.1\xi^\top\xi+\log\cosh(\xi)$ with $\Lambda=0$ along a contracting trajectory of the controller; the time derivative contains the term $\tfrac12\delta\xi^\top \frac{d}{dt}\nabla^2H_c(\xi)\delta\xi$, which is omitted in the proof of Theorem 4, and for this $H_c$ it can violate the required inequality, so the claimed bound $\leq 1/\epsilon_\delta$ would not hold.

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Extended reading notes

Core claim

The central claim is that the port-Hamiltonian controller (10) is dissipative for all parameters. Taking the Hamiltonian $H_c$ as the storage function and setting $\alpha = \epsilon \bar{\lambda}(G_cG_c^\top)$ makes the inequality $\dot H_c \leq -\epsilon\|y\|^2 + u^\top y$ hold algebraically, which is exactly $\epsilon$-output strict passivity and hence a finite $\mathcal{L}_2$ gain at most $1/\epsilon$ for any $J_c$, $\Lambda$, $G_c$, and $H_c$ (Theorem 3). Applying the same idea to the variational system with the Hessian $\nabla^2 H_c$ as the storage function, the paper claims that $0 < c_1 I \leq \nabla^2 H_c \leq c_2 I$ yields $\epsilon_\delta$-output strictly incremental passivity and a finite incremental $\mathcal{L}_2$ gain at most $1/\epsilon_\delta$ (Theorem 4). Discrete-gradient discretization of the same controller is claimed to preserve the $\epsilon$-output strict passivity and therefore the $\mathcal{L}_2$ bound (Theorem 5).

Load-bearing premise

The load-bearing premise is that knowing the curvature of the controller's energy function lies between two positive constants is enough to bound the incremental gain, because the proof does not control how fast that curvature changes along a trajectory.

Editorial extensions

If this is right

  • Distributed controllers in this class can be trained end-to-end with standard gradient-based methods, because the stability and gain certificates hold at every iteration and for the final parameters.
  • Communication constraints enter only through $G_c$ and the block structure of $J_c$, so the guarantee is inherited by sparse, neighbor-based controllers without any added constraints.
  • If the plant also has a known $\mathcal{L}_2$ or incremental gain, the small-gain theorem makes the closed-loop system stable with a computable bound, rather than only locally or after training.
  • The discrete-gradient discretization gives an implementable embedded controller whose $\mathcal{L}_2$ gain is preserved, unlike forward Euler, which can destroy passivity.

Reading between the lines

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

  • The incremental-gain proof implicitly requires a condition on how fast $\nabla^2 H_c$ changes along trajectories; adding a Lipschitz bound on $\nabla^2 H_c$ or a contraction analysis of the variational system would make the iL2 theorem robust, and such a condition is likely testable numerically during training.
  • Because the discrete-gradient update is implicit, deploying Theorem 5 in real time requires solving the fixed-point equation (17); guaranteeing existence and uniqueness is a separate numerical step, so the 'parameter-free' guarantee is only as strong as that solver.
  • In the robot consensus experiment the controller parameters are time-varying during the finite horizon and frozen afterward; one may infer that the a priori stability certificates fully cover the frozen regime, while collision-avoidance behavior during training is a learned property rather than a guaranteed one.
  • The same parametrization could be used for identification of distributed nonlinear systems with guaranteed $\mathcal{L}_2$ stability, since the gain bound holds for all weights and the sparsity pattern is fixed.
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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 a class of distributed port-Hamiltonian (pH) controllers whose storage functions can be parametrized by neural networks, and claims that this yields an unconstrained parametrization with a priori finite L2 or incremental L2 (iL2) gains. The L2 result (Theorem 3) is obtained by choosing the damping coefficient as α = ε λ̄(GcGcᵀ), making the controller ε-output strictly passive for all parameters. The iL2 result (Theorem 4) is obtained by applying the same damping choice to the variational dynamics and using a quadratic form in the Hessian as a differential storage function. The paper also presents a discrete-gradient discretization (Theorem 5) claimed to preserve the L2 passivity property, and two case studies: consensus of non-holonomic robots and voltage/power regulation in DC microgrids. The main iL2 claim is not established: the proof of Theorem 4 omits the time derivative of the Hessian in the storage function, and the theorem is in fact false as stated for a Hamiltonian satisfying its assumptions.

Significance. If Theorem 4 were correct, the paper would provide a genuinely attractive extension of unconstrained stable parametrizations to distributed nonlinear controllers with arbitrary strictly convex storage functions, going beyond quadratic-storage RENs. Theorem 3 and the discrete-gradient L2 preservation argument are valuable and appear sound, and the experimental section demonstrates that the proposed training pipeline can produce reasonable closed-loop behavior. However, the incremental-L2 contribution is the paper's central novelty in Section IV, underpins Remark 7 and the DC microgrid experiment, and the stated theorem has a concrete counterexample. Because the main iL2 guarantee is not merely unproved but false under the theorem's own hypotheses, the significance of the paper as a whole is substantially reduced. I also note that no code or data is provided, so the experimental results are not independently reproducible.

major comments (3)
  1. [Appendix B, Theorem 4]
  2. [Remark 7 and Section VI-B]
  3. [Section V, Eq. (17)]
minor comments (5)
  1. [Abstract]
  2. [Definitions 1 and 2]
  3. [Theorem 4 statement]
  4. [Section VI-A]
  5. [Appendix D]

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the L2/iL2 gain guarantees are structural dissipativity inequalities with damping chosen from Gc, not fitted outputs or self-citation-dependent claims.

full rationale

The derivation chain is self-contained. Theorem 3 establishes epsilon-output strict passivity by the standard pH storage inequality: with V=Hc, Vdot = gradH^T(J-(alpha I+Lambda))gradH <= -epsilon gradH^T Gc Gc^T gradH once alpha >= epsilon lambda_bar(Gc Gc^T), so the L2 gain <= 1/epsilon is a structural consequence of the damping choice, not an output of training. Theorem 4 is an analogous differential-dissipativity argument using Vdelta = 0.5 delta_xi^T Hessian(Hc) delta_xi and alpha >= epsilon_delta lambda_bar(Gc Gc^T); whatever the merit of the proof's treatment of the metric derivative, the claimed conclusion is not obtained by fitting parameters to data or by importing the result from the authors' prior work. Theorem 5 follows from the discrete-gradient chain rule and the same alpha choice. The self-citations ([3], [35], [36], [39], [46], [47]) are contextual comparisons or preliminary versions; none is load-bearing for Theorems 3-5, which cite standard external references [22], [45], [62], [78] for the passivity/dissipativity facts used. The training experiments are standard OCP/BPTT demonstrations, not predictions forced by a fitted constant. The proof gap in Theorem 4 identified by the reader is a correctness concern, not a circularity: the all-parameter iL2 bound may fail, but if so it fails because of an unjustified differentiation step, not because the theorem is assumed in its own proof.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard passivity results and on the assumption that the plant satisfies the small-gain or passivity conditions. The main unsupported step is the metric derivative term in Theorem 4, together with the deferred well-posedness of the implicit discrete scheme. No new physical entities are introduced.

free parameters (3)
  • ϵ (respectively ϵδ)
    User-chosen positive constant that sets the L2/iL2 gain bound 1/ϵ; not fitted to data.
  • Damping matrix Λ = e.g., 0.125 λ̄(GcGcᵀ) in robot, 10 I18 in microgrid, Λ ≡ 0 in robot
    Free trainable parameters; the iL2 theorem's validity depends on their magnitude, which the theorem does not constrain.
  • α multiplier = α = 0.125λ̄ in robot; α = 2.0λ̄ in microgrid
    Hand-chosen to set gain bounds; in the microgrid the implied ϵδ = 2.0 gives a claimed iL2 gain ≤ 0.5.
assumptions (5)
  • standard math Passivity and small-gain theorems from van der Schaft [22] are used without proof.
    Invoked in Theorem 1,2 and in the proofs of Theorems 3-5.
  • domain assumption The plant Σs is passive or has sufficiently small L2/iL2 gain.
    Closed-loop stability claims rely on the plant satisfying the conditions of Theorem 1 or 2; for the experiments this is asserted rather than verified with computed gains.
  • domain assumption Hamiltonian Hc is C2 and satisfies 0 < c1I ≤ ∇²Hc ≤ c2I (for Theorem 4).
    Needed for the variational storage to be positive definite; the log-cosh Hamiltonian in the microgrid satisfies this, but the proof still misses the metric derivative term.
  • ad hoc to paper Existence and uniqueness of solutions to the implicit discrete controller (17).
    The paper defers to [65] without stating or verifying the sufficient conditions, and the NNs used may not satisfy them.
  • standard math Differential dissipativity implies incremental dissipativity via [45, Theorem 6].
    Quoted to convert the variational passivity to an iL2 gain; the quoted result itself requires additional regularity not discussed in the paper.

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Pith. "Pith review of Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approach." pith.science (2026). https://pith.science/paper/N7YCCF3K

@misc{pith2026241110096,
  author       = {Pith},
  title        = {Pith review of: Neural Port-Hamiltonian Models for Nonlinear Distributed Control: An Unconstrained Parametrization Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/N7YCCF3K}},
  note         = {Machine review of arXiv:2411.10096}
}
abstract

The control of large-scale cyber-physical systems requires optimal distributed policies relying solely on limited communication with neighboring agents. However, computing stabilizing controllers for nonlinear systems while optimizing complex costs remains a significant challenge. Neural Networks (NNs), known for their expressivity, can be leveraged to parametrize control policies that yield good performance. However, NNs' sensitivity to small input changes poses a risk of destabilizing the closed-loop system. Many existing approaches enforce constraints on the controllers' parameter space to guarantee closed-loop stability, leading to computationally expensive optimization procedures. To address these problems, we leverage the framework of port-Hamiltonian systems to design continuous-time distributed control policies for nonlinear systems that guarantee closed-loop stability and finite $\mathcal{L}_2$ or incremental $\mathcal{L}_2$ gains, independent of the optimzation parameters of the controllers. This eliminates the need to constrain parameters during optimization, allowing the use of standard techniques such as gradient-based methods. Additionally, we discuss discretization schemes that preserve the dissipation properties of these controllers for implementation on embedded systems. The effectiveness of the proposed distributed controllers is demonstrated through consensus control of non-holonomic mobile robots subject to collision avoidance and averaged voltage regulation with weighted power sharing in DC microgrids.

Figures

Figures reproduced from arXiv: 2411.10096 by the authors.

Figure 1
Figure 1. An example of an interconnected system Σs and a distributed controller Σc for N = 4. The solid lines represent interactions between the subsystems of Σs, and the dashed lines represent the flow of information between the system Σs and the controller Σc. II. PROBLEM FORMULATION In this section, we formally formulate the distributed control problem of interest. To this end, we consider a network Σs of N coupled nonlin… view at source ↗
Figure 3
Figure 3. The mobile wheeled robot used in the experiment. The [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Forward velocities of the swarm demonstrating consen [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figures from the paper (9 more)
Figure 6
Figure 6. Figure 6: The electric scheme of i th DGU and the collocated load. [73]. An electrical circuit diagram of a typical DGU with its load is provided in [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 5
Figure 5. Figure 5: Relative distance rij among the agents with collision avoidance. Note that rij < 0.5 indicates a collision. The translucent blue color lines represent the evolution of trajec￾tories starting from the initial conditions sampled from a ball with radius 0.05 centered at t…
Figure 7
Figure 7. Figure 7: We consider loads modeled by an impedance and a [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 7
Figure 7. Figure 7: Representation diagram of the DC microgrid with [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 11
Figure 11. Figure 11: Voltages of individual DGUs. identification from data, where for example, the identified models are stable by design and have a finite L2 gain. Further efforts will be devoted to implementing the con￾trollers on real-world systems and also to generalize the framework …
Figure 9
Figure 9. Figure 9: Weighted averaged power converging to P ⋆ . 0.0 0.1 0.2 0.3 0.4 0.5 Time(sec) 35 40 45 50 55 Voltage (V) [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: Averaged voltage of the whole microgrid for 10 [PITH_FULL_IMAGE:figures/full_fig_p011_10.png]
Figure 12
Figure 12. Figure 12: Evolution of trajectories for a random initial condition. [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]
Figure 13
Figure 13. Figure 13: The comparison of the outputs of the pH controllers [PITH_FULL_IMAGE:figures/full_fig_p013_13.png]

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Reference graph

Works this paper leans on

80 extracted references · 58 canonical work pages

  1. [1]

    A counterexample in stochastic optimum control,

    H. S. Witsenhausen, “A counterexample in stochastic optimum control,” SIAM Journal on Control , vol. 6, no. 1, pp. 131–147, 1968

    work page 1968

  2. [2]

    Quadratic invariance is necessary and sufficient for convexity,

    L. Lessard and S. Lall, “Quadratic invariance is necessary and sufficient for convexity,” in IEEE American Control Conference (ACC) , 2011, pp. 5360–5362

    work page 2011

  3. [3]

    Distributed neural network control with dependability guarantees: a compositional port-Hamiltonian approach,

    L. Furieri, C. L. Galimberti, M. Zakwan, and G. Ferrari-Trecate, “Distributed neural network control with dependability guarantees: a compositional port-Hamiltonian approach,” in Learning for Dynamics and Control Conference. PMLR, 2022, pp. 571–583

    work page 2022

  4. [4]

    Safe learning in robotics: From learning-based control to safe reinforcement learning,

    L. Brunke, M. Greeff, A. W. Hall, Z. Yuan, S. Zhou, J. Panerati, and A. P. Schoellig, “Safe learning in robotics: From learning-based control to safe reinforcement learning,” Annual Review of Control, Robotics, and Autonomous Systems , vol. 5, pp. 411–444, 2022

    2022

  5. [5]

    Contraction theory for nonlinear stability analysis and learning-based control: A tutorial overview,

    H. Tsukamoto, S.-J. Chung, and J.-J. E. Slotine, “Contraction theory for nonlinear stability analysis and learning-based control: A tutorial overview,” Annual Reviews in Control , vol. 52, pp. 135–169, 2021

    2021

  6. [6]

    Safe control with learned certificates: A survey of neural Lyapunov, barrier, and contraction methods,

    C. Dawson, S. Gao, and C. Fan, “Safe control with learned certificates: A survey of neural Lyapunov, barrier, and contraction methods,” arXiv preprint arXiv:2202.11762, 2022

    arXiv 2022

  7. [7]

    Learning to boost the performance of stable nonlinear systems,

    L. Furieri, C. L. Galimberti, and G. Ferrari-Trecate, “Learning to boost the performance of stable nonlinear systems,” IEEE Open Journal of Control Systems, pp. 1–16, 2024

    work page 2024

  8. [8]

    Neural exponen- tial stabilization of control-affine nonlinear systems,

    M. Zakwan, L. Xu, and G. Ferrari-Trecate, “Neural exponen- tial stabilization of control-affine nonlinear systems,” arXiv preprint arXiv:2403.17793, 2024

    arXiv 2024

Show all 80 references
  1. [9]

    Physics- informed machine learning for modeling and control of dynamical systems,

    T. X. Nghiem, J. Drgo ˇna, C. Jones, Z. Nagy, R. Schwan, B. Dey, A. Chakrabarty, S. Di Cairano, J. A. Paulson, A. Carron et al., “Physics- informed machine learning for modeling and control of dynamical systems,” arXiv preprint arXiv:2306.13867 , 2023

    2023

  2. [10]

    Deep subspace encoders for nonlinear system identification,

    G. I. Beintema, M. Schoukens, and R. T ´oth, “Deep subspace encoders for nonlinear system identification,” Automatica, vol. 156, p. 111210, 2023

    2023

  3. [11]

    Recurrent equilibrium networks: Flexible dynamic models with guaranteed stability and ro- bustness,

    M. Revay, R. Wang, and I. R. Manchester, “Recurrent equilibrium networks: Flexible dynamic models with guaranteed stability and ro- bustness,” IEEE Transactions on Automatic Control , 2023

    2023

  4. [12]

    Physically consistent neural ODEs for learning multi-physics systems,

    M. Zakwan, L. Di Natale, B. Svetozarevic, P. Heer, C. N. Jones, and G. Ferrari-Trecate, “Physically consistent neural ODEs for learning multi-physics systems,” IFAC-PapersOnLine, vol. 56, no. 2, pp. 5855– 5860, 2023

    2023

  5. [13]

    Simba: System identification methods leveraging backpropagation,

    L. Di Natale, M. Zakwan, P. Heer, G. Ferrari-Trecate, and C. N. Jones, “Simba: System identification methods leveraging backpropagation,” arXiv preprint arXiv:2311.13889 , 2023

    2023 arXiv

  6. [14]

    Stable linear subspace identification: A machine learning approach,

    L. Di Natale, M. Zakwan, B. Svetozarevic, P. Heer, G. Ferrari-Trecate, and C. N. Jones, “Stable linear subspace identification: A machine learning approach,” arXiv preprint arXiv:2311.03197 , 2023

    2023 arXiv

  7. [15]

    Neural ordinary differential equation control of dynamics on graphs,

    T. Asikis, L. B ¨ottcher, and N. Antulov-Fantulin, “Neural ordinary differential equation control of dynamics on graphs,” Physical Review Research, vol. 4, no. 1, p. 013221, 2022

    2022

  8. [16]

    AI pontryagin or how artificial neural networks learn to control dynamical systems,

    L. B ¨ottcher, N. Antulov-Fantulin, and T. Asikis, “AI pontryagin or how artificial neural networks learn to control dynamical systems,” Nature communications, vol. 13, no. 1, p. 333, 2022

    2022

  9. [17]

    Cautious model predic- tive control using gaussian process regression,

    L. Hewing, J. Kabzan, and M. N. Zeilinger, “Cautious model predic- tive control using gaussian process regression,” IEEE Transactions on Control Systems Technology, vol. 28, no. 6, pp. 2736–2743, 2019

    2019

  10. [18]

    Model predictive control design for dynamical systems learned by echo state networks,

    L. B. Armenio, E. Terzi, M. Farina, and R. Scattolini, “Model predictive control design for dynamical systems learned by echo state networks,” IEEE Control Systems Letters , vol. 3, no. 4, pp. 1044–1049, 2019

    2019

  11. [19]

    On recurrent neural networks for learning-based control: recent results and ideas for future developments,

    F. Bonassi, M. Farina, J. Xie, and R. Scattolini, “On recurrent neural networks for learning-based control: recent results and ideas for future developments,” Journal of Process Control, vol. 114, pp. 92–104, 2022

    2022

  12. [20]

    Learning model predictive control with long short-term memory networks,

    E. Terzi, F. Bonassi, M. Farina, and R. Scattolini, “Learning model predictive control with long short-term memory networks,” International Journal of Robust and Nonlinear Control , vol. 31, no. 18, pp. 8877– 8896, 2021

    2021

  13. [21]

    Robust classification using contractive Hamiltonian neural ODEs,

    M. Zakwan, L. Xu, and G. Ferrari Trecate, “Robust classification using contractive Hamiltonian neural ODEs,” IEEE Control Systems Letters , vol. 7, pp. 145–150, 2022

    2022

  14. [22]

    van der Schaft, L2-Gain and Passivity Techniques in Nonlinear Control, 3rd ed., ser

    A. van der Schaft, L2-Gain and Passivity Techniques in Nonlinear Control, 3rd ed., ser. Communications and Control Engineering. Cham: Springer International Publishing, 2017

    2017

  15. [23]

    Communication topology co-design in graph recurrent neural network based distributed control,

    F. Yang and N. Matni, “Communication topology co-design in graph recurrent neural network based distributed control,” arXiv preprint arXiv:2104.13868, 2021

    2021 arXiv

  16. [24]

    Learning decentralized controllers for robot swarms with graph neural networks,

    E. Tolstaya, F. Gama, J. Paulos, G. Pappas, V . Kumar, and A. Ribeiro, “Learning decentralized controllers for robot swarms with graph neural networks,” in Conference on robot learning. PMLR, 2020, pp. 671–682

    2020

  17. [25]

    Graph policy gradients for large scale robot control,

    A. Khan, E. Tolstaya, A. Ribeiro, and V . Kumar, “Graph policy gradients for large scale robot control,” in Conference on robot learning. PMLR, 2020, pp. 823–834

    2020

  18. [26]

    Graph neural networks for distributed linear- quadratic control,

    F. Gama and S. Sojoudi, “Graph neural networks for distributed linear- quadratic control,” in Learning for Dynamics and Control . PMLR, 2021, pp. 111–124

    2021

  19. [27]

    Safe learning in robotics: From learning-based control to safe reinforcement learning,

    L. Brunke, M. Greeff, A. W. Hall, Z. Yuan, S. Zhou, J. Panerati, and A. P. Schoellig, “Safe learning in robotics: From learning-based control to safe reinforcement learning,” arXiv preprint arXiv:2108.06266, 2021

    2021 arXiv

  20. [28]

    End-to-end safe reinforcement learning through barrier functions for safety-critical continuous control tasks,

    R. Cheng, G. Orosz, R. M. Murray, and J. W. Burdick, “End-to-end safe reinforcement learning through barrier functions for safety-critical continuous control tasks,” in Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, no. 01, 2019, pp. 3387–3395

    2019

  21. [29]

    Safe model-based reinforcement learning with stability guarantees,

    F. Berkenkamp, M. Turchetta, A. P. Schoellig, and A. Krause, “Safe model-based reinforcement learning with stability guarantees,” Advances in Neural Information Processing Systems 30, vol. 2, pp. 909–919, 2018

    2018

  22. [30]

    The Lyapunov neural network: Adaptive stability certification for safe learning of dynamical systems,

    S. M. Richards, F. Berkenkamp, and A. Krause, “The Lyapunov neural network: Adaptive stability certification for safe learning of dynamical systems,” in Conference on Robot Learning . PMLR, 2018, pp. 466– 476

    2018

  23. [31]

    Learning-based model predictive control for safe exploration,

    T. Koller, F. Berkenkamp, M. Turchetta, and A. Krause, “Learning-based model predictive control for safe exploration,” in 2018 IEEE conference on decision and control (CDC) . IEEE, 2018, pp. 6059–6066

    2018

  24. [32]

    Offset- free setpoint tracking using neural network controllers,

    P. Pauli, J. K ¨ohler, J. Berberich, A. Koch, and F. Allg ¨ower, “Offset- free setpoint tracking using neural network controllers,” in Learning for dynamics and control . PMLR, 2021, pp. 992–1003

    2021

  25. [33]

    Learning deep energy shaping policies for stability-guaranteed manipulation,

    S. Abdulkhader, H. Yin, P. Falco, and D. Kragic, “Learning deep energy shaping policies for stability-guaranteed manipulation,” IEEE Robotics and Automation Letters , 2021

    2021

  26. [34]

    Hamiltonian-based neural ODE networks on the SE (3) manifold for dynamics learning and control,

    T. Duong and N. Atanasov, “Hamiltonian-based neural ODE networks on the SE (3) manifold for dynamics learning and control,” arXiv preprint arXiv:2106.12782, 2021

    2021 arXiv

  27. [35]

    Unconstrained parametrization of dissipative and contracting neural ordinary differential equations,

    D. Martinelli, C. L. Galimberti, I. R. Manchester, L. Furieri, and G. Ferrari-Trecate, “Unconstrained parametrization of dissipative and contracting neural ordinary differential equations,” arXiv preprint arXiv:2304.02976, 2023

    2023 arXiv

  28. [36]

    Unconstrained learning of networked nonlinear systems via free parametrization of sta- ble interconnected operators,

    L. Massai, D. Saccani, L. Furieri, and G. Ferrari-Trecate, “Unconstrained learning of networked nonlinear systems via free parametrization of sta- ble interconnected operators,” arXiv preprint arXiv:2311.13967 , 2023

    2023 arXiv

  29. [37]

    On the converse of the passivity and small-gain theorems for input–output maps,

    S. Z. Khong and A. van der Schaft, “On the converse of the passivity and small-gain theorems for input–output maps,” Automatica, vol. 97, pp. 58–63, 2018

    2018

  30. [38]

    A geometric integration approach to smooth optimisation: Foundations of the discrete gradient method,

    M. J. Ehrhardt, E. S. Riis, T. Ringholm, and C.-B. Sch ¨onlieb, “A geometric integration approach to smooth optimisation: Foundations of the discrete gradient method,” arXiv preprint arXiv:1805.06444 , 2018

    2018

  31. [39]

    Neural distributed controllers with port-Hamiltonian structures,

    M. Zakwan and G. Ferrari-Trecate, “Neural distributed controllers with port-Hamiltonian structures,” arXiv preprint arXiv:2403.17785 , 2024

    2024 arXiv

  32. [40]

    A Lyapunov approach to incremental stability properties,

    D. Angeli, “A Lyapunov approach to incremental stability properties,” IEEE Transactions on Automatic Control , vol. 47, no. 3, pp. 410–421, 2002

    2002

  33. [41]

    Analysis of interconnected oscillators by dissipativity theory,

    G.-B. Stan and R. Sepulchre, “Analysis of interconnected oscillators by dissipativity theory,” IEEE Transactions on Automatic Control , vol. 52, no. 2, pp. 256–270, 2007

    2007

  34. [42]

    Incremental stability properties for discrete-time systems,

    D. N. Tran, B. S. R ¨uffer, and C. M. Kellett, “Incremental stability properties for discrete-time systems,” in 2016 IEEE 55th Conference on Decision and Control (CDC) . IEEE, 2016, pp. 477–482

    2016

  35. [43]

    On the incremental form of dissipativity,

    R. Sepulchre, T. Chaffey, and F. Forni, “On the incremental form of dissipativity,” IFAC-PapersOnLine, vol. 55, no. 30, pp. 290–294, 2022

    2022

  36. [44]

    Arcak, C

    M. Arcak, C. Meissen, and A. Packard, Networks of dissipative sys- tems: compositional certification of stability, performance, and safety . Springer, 2016

    2016

  37. [45]

    Convex in- cremental dissipativity analysis of nonlinear systems,

    C. Verhoek, P. J. Koelewijn, S. Haesaert, and R. T ´oth, “Convex in- cremental dissipativity analysis of nonlinear systems,” Automatica, vol. 150, p. 110859, 2023

    2023

  38. [46]

    Hamil- tonian deep neural networks guaranteeing non-vanishing gradients by design,

    C. L. Galimberti, L. Furieri, L. Xu, and G. Ferrari-Trecate, “Hamil- tonian deep neural networks guaranteeing non-vanishing gradients by design,” IEEE Transactions on Automatic Control , pp. 1–8, 2023, doi: 10.1109/TAC.2023.3239430

    2023

  39. [47]

    Universal approxi- mation property of Hamiltonian deep neural networks,

    M. Zakwan, M. d’Angelo, and G. Ferrari-Trecate, “Universal approxi- mation property of Hamiltonian deep neural networks,” IEEE Control Systems Letters, vol. 7, pp. 2689–2694, 2023

    2023

  40. [48]

    Input convex neural networks,

    B. Amos, L. Xu, and J. Z. Kolter, “Input convex neural networks,” in International Conference on Machine Learning. PMLR, 2017, pp. 146– 155

    2017

  41. [49]

    Deep residual learning for image recognition,

    K. He, X. Zhang, S. Ren, and J. Sun, “Deep residual learning for image recognition,” in Proceedings of the IEEE conference on computer vision and pattern recognition , 2016, pp. 770–778

    2016

  42. [50]

    Nocedal and S

    J. Nocedal and S. J. Wright, Numerical optimization. Springer, 1999

    1999

  43. [51]

    Global convergence of admm in nonconvex nonsmooth optimization,

    Y . Wang, W. Yin, and J. Zeng, “Global convergence of admm in nonconvex nonsmooth optimization,” Journal of Scientific Computing , vol. 78, pp. 29–63, 2019

    2019

  44. [52]

    An augmented Lagrangian based algorithm for distributed nonconvex optimization,

    B. Houska, J. Frasch, and M. Diehl, “An augmented Lagrangian based algorithm for distributed nonconvex optimization,” SIAM Journal on Optimization, vol. 26, no. 2, pp. 1101–1127, 2016

    2016

  45. [53]

    Large-scale nonlinear programming using ipopt: An integrating framework for enterprise-wide dynamic optimization,

    L. T. Biegler and V . M. Zavala, “Large-scale nonlinear programming using ipopt: An integrating framework for enterprise-wide dynamic optimization,” Computers & Chemical Engineering , vol. 33, no. 3, pp. 575–582, 2009

    2009

  46. [54]

    Backpropagation through time: what it does and how to do it,

    P. J. Werbos, “Backpropagation through time: what it does and how to do it,” Proceedings of the IEEE , vol. 78, no. 10, pp. 1550–1560, 1990

    1990

  47. [55]

    Neu- ral ordinary differential equations,

    R. T. Q. Chen, Y . Rubanova, J. Bettencourt, and D. K. Duvenaud, “Neu- ral ordinary differential equations,” in Advances in Neural Information Processing Systems, S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett, Eds., vol. 31. Curran Associate...

    2018

  48. [56]

    Foucart and H

    S. Foucart and H. Rauhut, A Mathematical Introduction to Compressive Sensing, ser. Applied and Numerical Harmonic Analysis. Springer New York, 2013. [Online]. Available: https://books.google.ch/books? id=zb28BAAAQBAJ

    2013

  49. [57]

    Pytorch: An imperative style, high- performance deep learning library,

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Kopf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, and S. Chintala, “Pytorch: An imperative style, high- p...

    2019

  50. [58]

    Passivity indices and passivation of systems with application to systems with input/output delay,

    M. Xia, P. J. Antsaklis, and V . Gupta, “Passivity indices and passivation of systems with application to systems with input/output delay,” in 53rd IEEE Conference on Decision and Control . IEEE, 2014, pp. 783–788

    2014

  51. [59]

    Preserving and achieving passivity- short property through discretization,

    Y . Joo, R. Harvey, and Z. Qu, “Preserving and achieving passivity- short property through discretization,” IEEE Transactions on Automatic Control, vol. 65, no. 10, pp. 4265–4272, 2019

    2019

  52. [60]

    Interconnection of discrete-time dissipative systems,

    A. Martinelli, A. Aboudonia, and J. Lygeros, “Interconnection of discrete-time dissipative systems,” arXiv preprint arXiv:2311.08088 , 2023

    2023 arXiv

  53. [61]

    Geometric nu- merical integration,

    E. Hairer, M. Hochbruck, A. Iserles, and C. Lubich, “Geometric nu- merical integration,” Oberwolfach Reports, vol. 3, no. 1, pp. 805–882, 2006

    2006

  54. [62]

    Time integration and discrete Hamiltonian systems,

    O. Gonzalez, “Time integration and discrete Hamiltonian systems,” Journal of Nonlinear Science , vol. 6, pp. 449–467, 1996

    1996

  55. [63]

    On upstream differencing and godunov-type schemes for hyperbolic conservation laws,

    A. Harten, P. D. Lax, and B. v. Leer, “On upstream differencing and godunov-type schemes for hyperbolic conservation laws,” SIAM review, vol. 25, no. 1, pp. 35–61, 1983

    1983

  56. [64]

    Hamiltonian-conserving discrete canonical equa- tions based on variational difference quotients,

    T. Itoh and K. Abe, “Hamiltonian-conserving discrete canonical equa- tions based on variational difference quotients,” Journal of Computa- tional Physics, vol. 76, no. 1, pp. 85–102, 1988

    1988

  57. [65]

    Control design for a class of discrete-time Port- Hamiltonian systems,

    A. Macchelli, “Control design for a class of discrete-time Port- Hamiltonian systems,” IEEE Transactions on Automatic Control , 2023

    2023

  58. [66]

    Robust implicit networks via non-euclidean contractions,

    S. Jafarpour, A. Davydov, A. Proskurnikov, and F. Bullo, “Robust implicit networks via non-euclidean contractions,” Advances in Neural Information Processing Systems , vol. 34, pp. 9857–9868, 2021

    2021

  59. [67]

    Physics-informed implicit representations of equilibrium network flows,

    K. D. Smith, F. Seccamonte, A. Swami, and F. Bullo, “Physics-informed implicit representations of equilibrium network flows,” Advances in Neural Information Processing Systems , vol. 35, pp. 7211–7221, 2022

    2022

  60. [68]

    Ro- bustness certificates for implicit neural networks: A mixed monotone contractive approach,

    S. Jafarpour, M. Abate, A. Davydov, F. Bullo, and S. Coogan, “Ro- bustness certificates for implicit neural networks: A mixed monotone contractive approach,” in Learning for Dynamics and Control Confer- ence. PMLR, 2022, pp. 917–930

    2022

  61. [69]

    Monotone operator equilibrium networks,

    E. Winston and J. Z. Kolter, “Monotone operator equilibrium networks,” Advances in neural information processing systems, vol. 33, pp. 10 718– 10 728, 2020

    2020

  62. [70]

    Stabi- lization of discrete port-Hamiltonian dynamics via interconnection and damping assignment,

    A. Moreschini, M. Mattioni, S. Monaco, and D. Normand-Cyrot, “Stabi- lization of discrete port-Hamiltonian dynamics via interconnection and damping assignment,” IEEE Control Systems Letters , vol. 5, no. 1, pp. 103–108, 2020

    2020

  63. [71]

    Distributed IDA-PBC for a class of non- holonomic mechanical systems,

    A. Tsolakis and T. Keviczky, “Distributed IDA-PBC for a class of non- holonomic mechanical systems,” IFAC-PapersOnLine, vol. 54, no. 14, pp. 275–280, 2021

    2021

  64. [72]

    Port-Hamiltonian modelling of a differential drive mobile robot with reference velocities as inputs,

    J. Gimenez, C. Rosales, and R. Carelli, “Port-Hamiltonian modelling of a differential drive mobile robot with reference velocities as inputs,” in 2015 XVI Workshop on Information Processing and Control (RPIC) . IEEE, 2015, pp. 1–6

    2015

  65. [73]

    Consensus-based current sharing and voltage balancing in DC microgrids with exponential loads,

    P. Nahata, M. S. Turan, and G. Ferrari-Trecate, “Consensus-based current sharing and voltage balancing in DC microgrids with exponential loads,” IEEE Transactions on Control Systems Technology, vol. 30, no. 4, pp. 1668–1680, 2021

    2021

  66. [74]

    Power sharing in DC microgrids,

    V . Otten et al. , “Power sharing in DC microgrids,” Ph.D. dissertation, 2020

    2020

  67. [75]

    A scal- able port-Hamiltonian approach to plug-and-play voltage stabilization in DC microgrids,

    F. Strehle, M. Pfeifer, A. J. Malan, S. Krebs, and S. Hohmann, “A scal- able port-Hamiltonian approach to plug-and-play voltage stabilization in DC microgrids,” in 2020 IEEE Conference on Control Technology and Applications (CCTA). IEEE, 2020, pp. 787–794

    2020

  68. [76]

    Notions of input to output stability,

    E. D. Sontag and Y . Wang, “Notions of input to output stability,”Systems & Control Letters , vol. 38, no. 4-5, pp. 235–248, 1999

    1999

  69. [77]

    Review on control of DC microgrids and multiple microgrid clusters,

    L. Meng, Q. Shafiee, G. F. Trecate, H. Karimi, D. Fulwani, X. Lu, and J. M. Guerrero, “Review on control of DC microgrids and multiple microgrid clusters,” IEEE journal of emerging and selected topics in power electronics, vol. 5, no. 3, pp. 928–948, 2017

    2017

  70. [78]

    Port-Hamiltonian systems theory: An introductory overview,

    A. van der Schaft and D. Jeltsema, “Port-Hamiltonian systems theory: An introductory overview,” Foundations and Trends in Systems and Control, vol. 1, no. 2-3, pp. 173–378, 2014

    2014

  71. [79]

    Torchdyn: A neural differential equations library,

    M. Poli, S. Massaroli, A. Yamashita, H. Asama, and J. Park, “Torchdyn: A neural differential equations library,” arXiv preprint arXiv:2009.09346, 2020

    2009 arXiv

  72. [80]

    Adam: A method for stochastic gradient de- scent,

    D. P. Kingma and J. L. Ba, “Adam: A method for stochastic gradient de- scent,” in ICLR: International Conference on Learning Representations , 2015, pp. 1–15. Muhammad Zakwan is a doctoral assistant in the Dependable Control and Decision group (DE- CODE) at ´Ecole Polytechniqu...

    2015

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.