Quantifying and Visualizing Sim-to-Real Gaps: Physics-Guided Regularization for Reproducibility

Yuta Kawachi

REVIEW 5 major objections 4 minor 17 references

Quantifying and Visualizing Sim-to-Real Gaps: Physics-Guided Regularization for Reproducibility

T0 review · 5 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A gain-regularized, parameter-conditioned RNN matches simulation on real 110:1-gear hardware where naive domain randomization oscillates.

desk verdict Promising idea, but the hardware comparison is confounded by per-controller actuation scaling, post-hoc conditioning values, and filtered seeds. read the letter →

arxiv 2507.23445 v1 pith:PZXCBCR7 submitted 2025-07-31 cs.RO cs.SYeess.SY

Yuta Kawachi This is my paper

classification cs.ROcs.SYeess.SY

keywords sim-to-realgapdomainrandomizationphysics-guidedregularizationgain-equivalentRNNinvertedpendulumbalancingrobotparameter-conditionedpolicyreproduciblecontrol

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

The paper argues that for affordable robots with high gear ratios, closing the sim-to-real gap is better served by injecting simple physical measurements into training than by widening domain randomization. It proposes measuring the robot's effective proportional gains in a few real-world experiments and penalizing the RNN whenever its local input-output sensitivities drift from those values, while also feeding the current plant parameters to the controller so it does not collapse to an over-conservative average. On a two-wheeled balancing robot with a 110:1 gearbox, the resulting policy settles in hardware almost exactly as simulation predicts, whereas a purely domain-randomized policy oscillates persistently. If this holds, it gives robotics a lightweight path to reproducible transfer without expensive system identification.

What carries the argument

The key machinery is a physics-guided gain-regularization loss $L_{\mathrm{grad}} = \frac{1}{4}\sum_s |\mathbb{E}_{b,t}[\partial f/\partial s] - k_s|$, computed by automatic differentiation, where $k_s$ are measured proportional gains ($k_x, k_v, k_\theta, k_\omega$) from simple real-world experiments, combined with parameter-conditioned domain randomization that appends plant parameters to the RNN input. The loss anchors the network's local input-output sensitivities inside the real actuation envelope while conditioning lets it specialize per plant instead of averaging over all models.

What would settle it

Measure the real hardware's local force sensitivity by commanding small state offsets around balance and computing the actual $\partial f/\partial x$, $\partial f/\partial v$, $\partial f/\partial\theta$, and $\partial f/\partial\omega$ of the deployed RNN; the paper predicts the gain-regularized policy stays within the Table 3 working ranges while the naive DR-RNN exceeds them in angular velocity, so a deployment that violates this would falsify the gap-closing claim.

Watch

Extended reading notes

Core claim

The central discovery is that the equivalent gains of a neural controller—the averaged partial derivatives of its force output with respect to the state variables—can be treated as surrogates for the real plant's unknown dynamics, and constraining them to match measured proportional gains prevents the simulator from rewarding unrealistically aggressive virtual controllers. On the Balboa 32U4 platform, the gain-regularized, parameter-conditioned RNN reproduced simulated angular settling behavior in hardware, with matching peak times and decay envelopes, while the baseline domain-randomized RNN showed about 5 Hz oscillations and a clear sim-to-real timing mismatch.

Load-bearing premise

The central assumption is that a neural network's time- and batch-averaged partial derivatives with respect to the state can stand in for hand-tuned proportional gains, so that penalizing their deviation holds the policy inside the real actuation envelope; this equivalence is asserted rather than derived.

Editorial extensions

If this is right

Gain regularization suppresses the 'overly conservative policy' bias of domain randomization and preserves robustness near the nominal hardware parameters.
On the 110:1-gear balancing robot, the gain-constrained policy achieves hardware settling times that closely match simulation, while the purely domain-randomized policy shows persistent oscillations.
The sim-to-real gap can be visualized in plant-parameter space: naive domain randomization shifts the loss minimum toward 'easy' large-mass samples away from the true hardware, while the gain constraint recenters it.
The approach is lightweight and reproducible on off-the-shelf hardware, requiring only a few gain measurements instead of extensive system identification.
The equivalent gains of the constrained RNN remain below 2.0, whereas the domain-randomized RNN fluctuates between roughly 1.0 and 4.0, correlating with the observed hardware instability.

Reading between the lines

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

The same gain-equivalence idea could be extended to stiffness and damping sensitivities for contact-rich manipulation, treating measured local impedance profiles as regularization targets for neural policies.
Because the paper's best hardware results used out-of-domain damping context values, a natural next test is whether conditioning on the true measured values yields the same benefit; if not, the practical recipe would be to select the context that maximizes robustness rather than fidelity.
One could audit a deployed policy by probing its local input-output sensitivity at runtime, checking that it stays inside a measured hardware envelope as a reproducibility certificate for sim-to-real transfer.
The gain-regularization target could be made adaptive, updating the measured gains online as battery voltage or load changes, which might extend the approach beyond fixed-gain laboratory conditions.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Here's my take on Kawachi's paper. The core idea is worth a look: use measured PID gains as a regularizer for an RNN controller's local sensitivities, and condition the policy on plant parameters during domain randomization. The combination is new, even though the ingredients (PINN-style gradient penalties, conditioned DR) are known. The paper also contributes a nice visualization of how naive DR biases training toward 'easy' parameter samples and degrades performance near nominal, and the author is honest about limitations.

The main evidence doesn't hold up yet. The hardware comparison between DR-RNN and GC-DR-RNN uses different values of cemp in Eq. (11): 2.0 for DR, 1.5 for GC. The stress-test note says this gives DR 33% higher actuation gain, but if cemp scales inversely in the duty computation, the direction may be backwards. Regardless, the two controllers are deployed under different actuation calibrations, so the comparison is not controlled. The DR-RNN's oscillations could be a calibration artifact rather than evidence against domain randomization.

Second, the conditioning context values (Dc=17.06, Dp=0.0244) were chosen after the fact because they performed best, and they're out-of-domain. That undercuts the claim that conditioning on plant parameters works; the method was never tested at the true hardware parameters. Section 7.1 admits this, which is honest, but it's a load-bearing limitation.

Third, seed filtering is admitted in Section 7.3. Reporting only seeds that don't show instabilities is a problem, especially for a paper whose selling point is reproducibility. No code or data is provided either.

The 'gain-equivalent' interpretation is asserted rather than derived, but that's acceptable as an engineering heuristic; the real issue is that the evaluation isn't clean enough to validate it.

This paper is for researchers working on sim-to-real for high-gear-ratio, low-cost robots. It has a promising proposal and some useful visualizations, but the evaluation needs to be redone: constant cemp, conditioning at true parameters (or a clear justification for not doing so), all seeds reported, and code/data released. I'd send it to review with the expectation of major revision, not desk reject. The idea deserves scrutiny, but the current claims are not established.

Referee Report

5 major / 4 minor

Summary. The paper proposes a sim-to-real transfer method for a high-gear-ratio balancing robot. The method combines two ingredients: (i) a gain-regularization loss that penalizes deviation of a recurrent neural network controller's time- and batch-averaged input-output sensitivities from proportional gains measured on the real hardware, and (ii) parameter-conditioned domain randomization in which simulated plant parameters are appended to the controller input. The central claim is that this gain-regularized, parameter-conditioned RNN (GC-DR-RNN) achieves angular settling times in hardware that closely match simulation, whereas a purely domain-randomized RNN (DR-RNN) shows persistent oscillations and a large sim-to-real gap. The paper reports simulation contours, hardware roll-angle and angular-velocity time series, and qualitative recovery comparisons for the three controllers.

Significance. If the main claim were established, the paper would offer a lightweight and affordable recipe for closing the sim-to-real gap on non-backdrivable, high-gear-ratio robots, where naive domain randomization is known to struggle. The authors deserve credit for choosing a real low-cost platform, for measuring proportional gains on the actual hardware, and for explicitly acknowledging several limitations in Section 7, including the mismatch between conditioning context and true plant parameters, performance parity with a tuned proportional controller, and remaining seed sensitivity. The parameter-space contour plots and equivalent-gain visualizations are potentially useful diagnostic tools. However, the manuscript does not provide machine-checked proofs, reproducible code, or quantitative hardware metrics, and the central comparison is confounded by per-controller actuation calibration and post hoc selection of conditioning values. As it stands, the evidence does not establish the advertised claim.

major comments (5)

[Section 2.4, Eq. (11)] Equation (11) defines the motor force with a per-controller empirical scale cemp, taking values 1.2 for the proportional controller, 2.0 for the DR-RNN, and 1.5 for the GC-DR-RNN. Because cemp multiplies the entire commanded force, the DR-RNN is operated with roughly 33% higher actuation gain than the GC-DR-RNN (2.0/1.5) and about 67% higher than the proportional controller. The persistent oscillations attributed to the DR-RNN in Section 5 could therefore be caused by an overdriven actuation calibration rather than by the absence of gain regularization. The comparison in Figures 15-20 is not controlled unless a single cemp is used or the authors demonstrate invariance of the result to cemp.
[Sections 4 and 7.1] The conditioning context values Dc = 17.06 kg/s and Dp = 0.0244 Nms/rad are outside the domain-randomization range used during training (which is U(0.5,2.0) times Dc_nom = 3 kg/s and Dp_nom = 0.007 Nms/rad) and were selected because they gave the best simulated performance. This means the parameter-conditioning component was not evaluated at the true or even nominal hardware parameters that the method is supposed to use. The admitted limitation in Section 7.1 is directly load-bearing for the claim that conditioning on current plant parameters closes the sim-to-real gap; an evaluation at measured or at least nominal context values is required.
[Section 7.3] The paper states that only a few reruns were kept, filtering out 'classical-control-style instabilities.' No seed counts, failure rates, or selection criteria are reported. Without a deterministic seed protocol or a report of all outcomes, the hardware and simulated traces in Section 5 could be cherry-picked, and the claim that the GC-DR-RNN 'closely matches simulation' is not statistically supported.
[Section 2.3, Eq. (10)] The core physical assumption is that the time- and batch-averaged partial derivatives Eb,t[∂f/∂x], etc., of a nonlinear RNN are valid surrogates for linear PID gains and that penalizing their deviation keeps the policy inside the real actuation envelope. This equivalence is asserted rather than derived. Because the penalty applies to averaged derivatives, a network could satisfy Eq. (10) while having large pointwise sensitivity fluctuations that violate the intended actuation limits. A derivation, a pointwise-gain diagnostic, or an ablation that checks the constraint's satisfaction would be needed to support this load-bearing assumption.
[Section 5] The abstract and Section 5 claim that angular settling times in hardware closely match simulation, but no numeric settling-time values, confidence intervals, or trial counts are reported; Figures 15-20 are qualitative. A quantitative table with simulated versus measured settling times, peak values, and variability across runs is required to substantiate the headline claim.

minor comments (4)

[Section 2.2] The notation in Eq. (6) is ambiguous: the dimensions of C and the role of the 'reverse function' introduced in Section 2.4 are not defined, making the force-to-duty mapping difficult to reproduce.
[Section 3.3] Table 3 does not describe how the working proportional gains and their bounds were measured on the real robot, how many trials were used, or how the pre-experiments were protocolized; this information is necessary to reproduce the regularization targets.
[Figures 15-20] The hardware time-series figures lack a clear description of the experimental protocol, including trial duration, number of trials, sensor filtering details, and whether the traces are single trials or averaged; consistent axis labels and units should also be added.
[General] The paper frames the framework as 'reproducible' but provides no code repository, model weights, or data archive; a reproducibility statement or artifact link is needed.

Circularity Check

2 steps flagged · score 6.0 of 10

Hardware validation is partly fitted: the conditioning context was selected for best simulated settling time and each controller uses its own fitted actuation scaling cemp, so the headline sim-to-real comparison is not a controlled prediction.

fitted input called prediction [Section 4 (Simulated Results, friction-plane analysis) and Section 7.1]
"Thus, we selected out-of-domain context values of Dc = 17.06351 kg/s, Dp = 0.024376 Nms/rad for the experiments."

The conditioned inputs are supposed to be the current plant parameters, but the values used for the hardware experiments were chosen because they produced the best simulated settling-time contours; Sec. 7.1 admits the 'best' performance did not occur at the hardware parameters. The hardware run therefore evaluates a context fitted to the success metric, not a prediction at the true plant. The reported sim-to-real match is partly a restatement of the selection criterion, and the parameter-conditioning component is untested at the parameters it claims to use.
fitted input called prediction [Section 2.4, Eq. (11)]
"Each constant is determined from datasheets or rough estimates and cemp absorbs modeling error. The cemp values are 1.2 (proportional control), 2.0 (only domain-randomized RNN), and 1.5 (gain-constrained domain-randomized RNN)."

cemp is a per-controller multiplier on the commanded force. With cemp=2.0 for DR-RNN and 1.5 for GC-DR-RNN, the DR policy is commanded with roughly 33% larger actuation gain. The paper's hardware conclusion—that DR-RNN oscillates and has a large sim-to-real gap while GC-DR-RNN transfers—is therefore not a controlled comparison; the difference could be produced by the separately fitted actuation scaling. The 'prediction' about which controller transfers is entangled with a fitted calibration constant.

full rationale

The paper's derivation chain is mostly self-contained: the RNN training, gain-regularization loss, and conditioning are defined directly from the plant model and measured gains, and there is no load-bearing self-citation chain (the self-cited [8] supplies an RNN architecture detail and is not central to the sim-to-real claim). The gain-equivalence assumption (treating ∂f/∂s as surrogate for PID gains) is a modeling assertion rather than a circularity. However, the empirical validation contains fitted inputs that are then reported as predictions. The conditioning context used in hardware was selected after seeing the simulated settling-time landscape (best out-of-domain values), and Sec. 7.1 concedes these are not the hardware values, so the parameter-conditioning claim is not tested at the true plant parameters. Additionally, the force-to-duty calibration constant cemp is fit independently for each controller, giving DR-RNN a 33% higher actuation gain; this confound means the DR-RNN's oscillations and the apparent advantage of gain regularization are not identified separately from the calibration difference. These are fit-dependent, not first-principles, results; the central claim therefore has partial circularity, but real hardware measurements keep it from being fully forced.

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

The method contributes measurements (PID gains) and a training loss, but it pulls several key assumptions from thin air: the equivalence between a network's averaged input-output derivatives and linear gains, the sufficiency of a simplified cart-pole/viscous-friction model, and the accuracy of a per-controller calibrated DC motor model. The free parameters that affect the central comparison are the per-controller cemp factors and the post-hoc selected context values.

free parameters (4)

cemp (empirical motor scaling per controller) = 1.2 (proportional), 2.0 (DR-RNN), 1.5 (GC-DR-RNN)
Scaling factors absorbing modeling error in the simplified DC motor model; different values per controller confound the sim-to-real comparison.
Conditioning context damping values = Dc=17.06351 kg/s, Dp=0.024376 Nms/rad
Selected because they gave best simulated performance, out-of-domain values not measured on the real robot; contradicts the idea of conditioning on true plant parameters.
Nominal proportional gains for regularization = kx=13 N/m, kv=15 N/(m/s), ktheta=31 N/rad, komega=1.6 N/(rad/s)
Hand-tuned in pre-experiments on the real robot; used as regression targets in the loss; measurement protocol not described in detail.
Nominal plant parameters = M=0.4 kg, m=0.3 kg, l=0.05 m, Dc=3 kg/s, Dp=0.007 Nms/rad
Set by empirical tuning; domain randomization ranges are centered on these values.

assumptions (4)

domain assumption Planar cart-pole model with no wheel slip and viscous friction only.
Section 2.1 states this simplification; if backlash, stiction, or wheel slip dominate on the 110:1-gearbox robot, the simulator used for training is not faithful to the plant.
ad hoc to paper Measured linear PID gains are valid surrogates for unmodeled plant dynamics (backlash, friction, gear-train bandwidth).
Section 2.3: 'We reinterpret proportional gains... as surrogates for the complex nature of unmodeled plant characteristics.' This is the paper's core interpretive leap.
ad hoc to paper Matching time-batch-averaged partial derivatives of the RNN to those gains is sufficient to keep the policy within the feasible actuation envelope.
Section 2.3: 'This constraint implicitly reflects real-world actuation characteristics...' The equivalence is asserted, not demonstrated.
domain assumption The simplified DC motor model with a single per-controller gain cemp accurately predicts real force output.
Section 2.4 Eq. (11) uses datasheet estimates plus a hand-adjusted cemp; the model's adequacy is assumed.

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Cite this review

Pith. "Pith review of Quantifying and Visualizing Sim-to-Real Gaps: Physics-Guided Regularization for Reproducibility." pith.science (2026). https://pith.science/paper/PZXCBCR7

@misc{pith2026250723445,
  author       = {Pith},
  title        = {Pith review of: Quantifying and Visualizing Sim-to-Real Gaps: Physics-Guided Regularization for Reproducibility},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PZXCBCR7}},
  note         = {Machine review of arXiv:2507.23445}
}

read the original abstract

Simulation-to-real transfer using domain randomization for robot control often relies on low-gear-ratio, backdrivable actuators, but these approaches break down when the sim-to-real gap widens. Inspired by the traditional PID controller, we reinterpret its gains as surrogates for complex, unmodeled plant dynamics. We then introduce a physics-guided gain regularization scheme that measures a robot's effective proportional gains via simple real-world experiments. Then, we penalize any deviation of a neural controller's local input-output sensitivities from these values during training. To avoid the overly conservative bias of naive domain randomization, we also condition the controller on the current plant parameters. On an off-the-shelf two-wheeled balancing robot with a 110:1 gearbox, our gain-regularized, parameter-conditioned RNN achieves angular settling times in hardware that closely match simulation. At the same time, a purely domain-randomized policy exhibits persistent oscillations and a substantial sim-to-real gap. These results demonstrate a lightweight, reproducible framework for closing sim-to-real gaps on affordable robotic hardware.

Figures

Figures reproduced from arXiv: 2507.23445 by the authors.

**Figure 2.** Control system architecture: state estimates (position, velocity, angle, angular velocity) are com [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Physical experimental platform: a two-wheeled inverted-pendulum robot (Balboa 32U4) equipped [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (17 more)

**Figure 4.** Figure 4: Normalized training loss over 4000 epochs for two controllers: the domain-randomized RNN [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Zoom into the first 400 epochs of the normalized training loss. The GC-DR-RNN (red) converges [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: Suppression of sim-specific equivalent-gain [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: 5% settling-time contours of the proportional controller over the cart mass [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]

**Figure 8.** Figure 8: 5% settling-time contours of the DR-RNN over the cart mass [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]

**Figure 9.** Figure 9: 5% settling-time contours for the GC-DR-RNN over the cart mass [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

**Figure 10.** Figure 10: Final minibatch sample locations (orange dots) overlaid on the contour map of angular velocity [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]

**Figure 11.** Figure 11: Final minibatch sample locations (orange dots) overlaid on the contour map of angular velocity [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]

**Figure 12.** Figure 12: Angular 5% settling-time contours of the GC-DR-RNN across viscous damping parameters [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]

**Figure 13.** Figure 13: Angular 5% settling-time contours when conditioning the GC-DR-RNN on twice the nominal [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]

**Figure 14.** Figure 14: Angular 5% settling-time contours when the GC-DR-RNN is trained with extreme (out-of-domain) [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]

**Figure 15.** Figure 15: Real-world roll-angle responses under three controllers: proportional (green dashed), DR-RNN [PITH_FULL_IMAGE:figures/full_fig_p018_15.png]

**Figure 16.** Figure 16: Measured angular velocity traces: the DR-RNN (gray) oscillates beyond [PITH_FULL_IMAGE:figures/full_fig_p018_16.png]

**Figure 17.** Figure 17: Zoom into 10–20 s of angular velocity data. The DR-RNN retains persistent [PITH_FULL_IMAGE:figures/full_fig_p019_17.png]

**Figure 18.** Figure 18: Simulated vs. real angular velocity recovery for the proportional controller. Peak times and decay [PITH_FULL_IMAGE:figures/full_fig_p020_18.png]

**Figure 19.** Figure 19: Simulated vs. real angular velocity recovery for the DR-RNN: while simulation predicts fast [PITH_FULL_IMAGE:figures/full_fig_p021_19.png]

**Figure 20.** Figure 20: Simulated vs. real angular velocity recovery for the GC-DR-RNN: both domains show nearly [PITH_FULL_IMAGE:figures/full_fig_p022_20.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

W. Cha, J. Cha, J. Shin, D. Kim, and J. Park. Sim-to-real of humanoid locomotion policies via joint torque space perturbation injection. arXiv:2504.06585, 2025. 9 Figure 7: 5% settling-time contours of the proportional controller over the cart mass M vs. pole mass m plane. Fast convergence (dark blue) is confined to a narrow band around the nominal parame...

arXiv 2025

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Chane-Sane, J

E. Chane-Sane, J. Amigo, T. Flayols, L. Righetti, and N. Mansard. Soloparkour: Constrained rein- forcement learning for visual locomotion from privileged experience. In Conference on Robot Learning. arXiv, 2024

work page 2024

[3] [3]

Giacomuzzo, R

G. Giacomuzzo, R. Carli, D. Romeres, and A. Dalla Libera. A black-box physics-informed estimator based on gaussian process regression for robot inverse dynamics identification. IEEE Transactions on Robotics, 2024

work page 2024

[4] [4]

C. D. Green. Equations of motion for the cart and pole control task. Technical report, January 2020

work page 2020

[5] [5]

T. He, J. Gao, W. Xiao, Y. Zhang, Z. Wang, J. Wang, Z. Luo, G. He, N. Sobanbab, C. Pan, et al. Asap: Aligning simulation and real-world physics for learning agile humanoid whole-body skills. arXiv:2502.01143, 2025

arXiv 2025

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T. He, Z. Luo, W. Xiao, C. Zhang, K. Kitani, C. Liu, and G. Shi. Learning human-to-humanoid real- time whole-body teleoperation. In 2024 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 8944–8951. IEEE, 2024

work page 2024

[7] [7]

Learning Bipedal Locomotion on Gear-Driven Humanoid Robot Using Foot-Mounted IMUs

S. Katayama, Y. Koda, N. Nagatsuka, and M. Kinoshita. Learning bipedal locomotion on gear-driven humanoid robot using foot-mounted imus. arXiv:2504.00614, 2025. 10 Figure 8: 5% settling-time contours of the DR-RNN over the cart mass M vs. pole mass m plane: the stable region is substantially wider than the proportional baseline, but the nominal point lies...

work page Pith review arXiv 2025

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PMSM transient response optimization by end-to-end optimal control

Y. Kawachi, M. Ambai, Y. Yoshida, and G. Takano. Pmsm transient response optimization by end-to- end optimal control. arXiv:2402.03820, 2024

work page Pith review arXiv 2024