Imitation Learning for Satellite Attitude Control under Unknown Perturbations

Hao Peng; Xiaoli Bai; Zhizhuo Zhang

REVIEW 4 major objections 8 minor 19 references

Imitation Learning for Satellite Attitude Control under Unknown Perturbations

T0 review · 4 major / 8 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that a reward-shaped Soft Actor-Critic controller and a GAIL imitation learner can reorient a satellite antenna under unknown torque, alignment, and gyroscope faults, and that imitation reduces training cost.

desk verdict A plausible SAC-vs-DDPG comparison with a genuine imitation-learning application, but the central GAIL sample-complexity claim rests on an invalid reward comparison and needs a rewrite before it can be taken seriously. read the letter →

arxiv 2507.01161 v1 pith:QWEOO2Q4 submitted 2025-07-01 eess.SY cs.ROcs.SY

Zhizhuo Zhang , Hao Peng , Xiaoli Bai This is my paper · ORCID

classification eess.SYcs.ROcs.SY

keywords satelliteattitudecontrolSoftActor-CriticGenerativeAdversarialImitationLearningreinforcementspacecraftperturbationantennareorientationrewardshaping

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 seeks to show that satellite attitude control under unknown perturbations can be handled by a two-stage learning pipeline: first train a Soft Actor-Critic (SAC) controller as an expert, then train another agent to imitate the expert's trajectories with Generative Adversarial Imitation Learning (GAIL). The motivation is that model-based controllers need accurate system models, while pure reinforcement learning is sample-hungry. The paper claims the SAC expert outperforms an earlier DDPG controller under torque failures, torque noise plus attitude misalignment, and gyroscope noise, and that the GAIL learner reaches similar duty-cycle and RMS performance while earning higher reward early in training. If true, this is evidence that imitation learning can transfer fault-tolerant attitude recovery policies with less online interaction.

What carries the argument

The argument runs on three coupled pieces. The first is the SAC update rule, whose entropy-regularized objective and dual critics give a stochastic policy able to keep exploring under perturbations. The second is the shaped reward function in Eq. (15), which combines an exponential attitude-error reward, a control-effort penalty, a regression penalty, a stay bonus inside 5 degrees, and a large terminal penalty for angular velocities above 10 degrees per second. The third is the GAIL discriminator, which assigns the implicit reward $r(s,a)=-\log D_\omega(s,a)$, so the learner is pushed to produce state-action pairs the discriminator cannot separate from the expert. The discriminator-based reward is the mechanism that lets the learner inherit the expert's behavior without accessing the handcrafted reward.

What would settle it

For each perturbation case, count the number of environment interactions the expert and the learner need to reach a fixed attitude accuracy, for instance RMS error below 15 degrees and duty cycle above 0.9; if the learner needs at least as many interactions as the expert, the sample-complexity claim is falsified.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that a reward-shaped SAC agent is a better expert for the antenna-reorientation task than the prior deterministic-policy controller, and that a second SAC agent trained with GAIL on that expert's trajectories reproduces most of its behavior. The expert is evaluated across fourteen perturbation cases, including single and two-axis torque failures, constant attitude misalignment, torque noise, gyroscope white noise, and gyroscope drift; the learner is trained and evaluated on ten of these cases and improves early-training mean reward in all of them. The paper also reports that replacing the handcrafted reward or switching from SAC back to DDPG degrades performance, supporting reward shaping and the stochastic policy as the carriers of the gain.

Load-bearing premise

The claim that GAIL reduces sample complexity assumes that the learner's mean reward during training can be compared with the expert's mean reward, even though the learner optimizes a different discriminator-based reward than the expert's handcrafted one; if the two reward scales are not comparable, a higher early reward curve does not by itself prove faster learning.

Editorial extensions

If this is right

A reward-shaped SAC controller can keep a CubeSat-like satellite's antenna within 10 degrees of the target under single-axis and some two-axis torque failures, torque noise with misalignment, and gyroscope noise, across most tested initial states.
A GAIL learner trained on that expert's trajectories matches or approaches the expert on duty cycle and RMS error in the baseline, torque-noise-plus-misalignment, single-torque-failure, and gyroscope-noise cases.
The learner inherits the expert's blind spots: cases where the expert itself fails, such as constant gyroscope bias or certain two-axis failures, are excluded from imitation training.
Ablations imply that both SAC and the refined reward in Eq. (15) are necessary for the expert's advantage; removing either reverts to the earlier controller's failure modes.

Reading between the lines

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

A stricter sample-complexity test would report environment steps to a fixed control performance, not early reward; that number is absent from the paper, so the reduction claim is not yet quantified.
Because a dedicated learner is trained for each perturbation case, the pipeline does not yet demonstrate one policy that generalizes across all fault modes; a single learner trained on mixed expert trajectories would be a natural next test.
The GAIL implicit reward could be combined with a fraction of the original handcrafted reward to stabilize training in drift and constant-bias cases where the expert's trajectories are sparse or unsuccessful.

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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

The paper is worth a read for its empirical comparison of SAC against the authors' earlier DDPG controller on a satellite antenna reorientation task. The SAC expert does appear to handle several perturbation cases better than the earlier work, and the ablation studies in Appendices C and D are a genuine effort to isolate the contributions of the reward redesign and the algorithm change. The application of GAIL to this specific attitude control problem is new, and the learner does track the expert's behavior on several experiments, which is a legitimate demonstration of imitation in a space-domain simulator. I agree with the reader that this is not a new algorithm; it is a new application of standard tools, and the literature review is honest about that.

The soft spot is the sample-complexity claim. Figure 9 plots the mean reward during training for the GAIL learner and the SAC expert, and the paper takes the learner's higher early curve as evidence of 'dramatically decreasing sample complexity.' That comparison is not commensurable: the learner optimizes a discriminator-based reward, r = -log D(s,a), while the expert optimizes the handcrafted reward of Eq. (15), which has different scale, a stay bonus, and a large termination penalty. A higher value of -log D near 0.7 at the start tells you the discriminator is uncertain, not that the learner is learning the task faster. The paper also never reports environment-step counts; mean reward is not a sample-complexity metric. So the central claim in the abstract and conclusion is unsupported as written. This is a load-bearing flaw for the GAIL part of the story, though it does not sink the entire paper.

Other issues: the quantitative tables use a single evaluation run averaged over six initial states, with no error bars or multiple seeds, so the reported differences between learner and expert could be noise. The paper also omits code and data, which matters for reproducibility of a simulation study. The authors themselves note that GAIL hyperparameters vary per experiment, which is a bit of a red flag for the method's robustness. On the citation pattern, the paper builds on the authors' own prior work, but that is appropriate given they are genuinely extending it; I do not see self-citation as a problem here.

I would not reject the paper outright. The SAC expert comparison is a plausible contribution, and the GAIL question is worth answering properly. But the sample-complexity claim needs to be redone with a matched reward scale or, better, with environment steps to reach a fixed duty-cycle or RMS threshold. The authors should also add multiple seeds and release code and data. With those changes, the paper could be acceptable. For now, it is a conditional at best.

I would send it to review, because the empirical work is substantial enough to deserve referee time, but I would be explicit to the authors that the current GAIL efficiency claim is not supported.

Referee Report

4 major / 8 minor

Summary. This paper proposes a two-stage learning framework for satellite antenna reorientation under unknown perturbations. A Soft Actor-Critic (SAC) agent is first trained with a handcrafted reward to act as an expert controller, and a second SAC agent is then trained with Generative Adversarial Imitation Learning (GAIL) using the expert's trajectories. Experiments in MuJoCo cover a baseline, single and double torque failures, attitude misalignment, and gyroscope noise, constant error, and drift. The paper claims that the SAC expert outperforms a prior DDPG controller and that the GAIL learner reduces sample complexity while imitating most of the expert's behavior.

Significance. If substantiated, the paper would provide a useful empirical demonstration that reinforcement learning combined with imitation learning can recover satellite attitude control under actuator and sensor perturbations. It includes a clear task formulation, quantitative evaluation metrics, and ablation studies for both the reward function and the learning algorithm. However, the central efficiency claim currently rests on an incommensurable reward comparison, and the imitation claim is only partially supported by the reported tables. The contribution is therefore promising but not yet established at the level claimed.

major comments (4)

[Performance of the Learner during Training; Figure 9; Eq. (5), Eq. (15)] The claim that GAIL 'dramatically decreases sample complexity' is not supported by the presented evidence. Figure 9 plots the learner's mean discriminator reward r(s,a) = -log D(s,a) (Eq. 5) against the expert's mean handcrafted reward (Eq. 15). These two reward signals are on different scales and are not commensurable, so a higher early curve for the learner does not imply faster task learning. Moreover, no environment-step counts are reported, and mean reward is not a sample-complexity metric. The authors should instead compare the number of environment steps (or episodes) required by the learner and the expert to reach a fixed task-performance level, such as duty cycle above a stated threshold or RMS below a stated threshold, using the same evaluation metric for both.
[Performance of the Learner in Experiments; Tables 2-6] The quantitative tables only partially support the claim that the learner 'can imitate most of the features' of the expert. In several experiments the learner is substantially worse: in Table 4, Experiment 3 has RMS 19.81 deg versus 6.61 deg and duty cycle 0.930 versus 0.990, and Experiment 4 has RMS 25.82 deg versus 14.21 deg and duty cycle 0.603 versus 0.867; in Table 5, Experiment 6 has RMS 15.08 deg versus 8.54 deg; in Table 6, Experiment 11 has RMS 18.29 deg versus 10.96 deg and duty cycle 0.855 versus 0.973. These are not small discrepancies, and the text's qualitative descriptions such as 'slightly worse' or 'not much different' understate them. Please quantify the fraction of experiments in which the learner meets a specified performance criterion, or revise the imitation claim to acknowledge the cases where imitation clearly degrades performance.
[Experiments and Results; Appendix B; Contribution 1] The claimed superiority of the SAC expert over Hao et al.'s DDPG controller [9] is established only by visual inspection of figures reprinted from the prior work. Since beating that baseline is contribution 1, the authors should provide quantitative metrics (duty cycle, RMS, max/min error) for the same DDPG baseline under the same evaluation protocol, or re-run the baseline and report its metrics. Without this, the comparison cannot be assessed by the reader and the claim is not falsifiable from the presented data.
[Formulation of the GAIL algorithm; Eq. (4)-(5), Algorithm 1] The description of the discriminator's meaning is internally inconsistent. The text says D(s,a) is the probability that a pair originated from the learner, but then states that 'if the discriminator perceives a learner-generated pair as expert-like, D(s,a) approaches unity'. Under the stated definition, an expert-like pair should make D close to zero, not one. Also, the sign conventions in Eq. (4), Eq. (5), and Algorithm 1 should be checked for mutual consistency, since the reward signal r(s,a) = -log D(s,a) is central to the GAIL experiments. Please clarify which convention is used (e.g., D high for expert samples versus D high for learner samples) and correct the text accordingly.

minor comments (8)

[Multiple experiment sections] There are numerical typos in iteration counts: '200,0000', '400,0000', and '100,0000' should presumably be 2,000,000, 4,000,000, and 1,000,000.
[Figure 9] The axes in Figure 9 are not labeled; specify the x-axis quantity (episodes, environment steps, or iterations) and the exact reward definition used for each curve.
[Perturbations Parameters, Eq. (9)] The notation for gyroscope noise standard deviation is inconsistent: Eq. (9) uses sigma_omega, while the text later reports sigma_eta = 0.1 deg/s.
[Performance of the Learner during Training] The text refers to 'Figure 12(b) and Figure 12(b)', which should be 'Figure 12(b) and Figure 12(c)'.
[SAC Algorithm Configuration, Eq. (15)] Equation (15) uses the symbol phi_t without defining it in the reward section; please define it as the angular difference between the antenna pointing direction and the target direction.
[Limitation and Future Work] The GAIL hyperparameters are said to vary per experiment, but the per-experiment values are not reported; please include them for reproducibility.
[Quantitative Evaluation Metrics] The six 'randomly generated initial states' are not specified; please report the distributions or exact initial conditions used so that the results can be reproduced.
[References] Reference [10] (Maximilian) is incomplete; provide the full publication venue and year.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the empirical comparisons are self-contained, and the weak sample-complexity argument is an evidentiary limitation rather than a circular reduction.

full rationale

The paper's load-bearing claims are empirical benchmark results, not derivations from inputs. The SAC expert is trained with the handcrafted reward of Eq. (15) and then tested under the perturbations listed in Table 1; the comparison against Hao et al. [9] is a baseline comparison to a published prior study, and the ablation studies in Appendix C independently vary the algorithm (DDPG vs SAC) and the reward function, so the expert's claimed improvement is not defined in terms of the prior work. The GAIL learner is trained on expert trajectories using the standard discriminator reward of Eq. (5), and its success is then assessed by the same quantitative metrics (duty cycle, RMS, max/min angle error) on the same task; this is an evaluation of a trained policy, not a prediction that is numerically equal to its training signal. The main weakness is the 'sample complexity' conclusion, which is inferred from Figure 9 by comparing the mean rewards of two different reward functions (Eq. 5 vs Eq. 15); that comparison is not a valid sample-complexity measurement, and no environment-step counts are reported. This is a real evidentiary limitation but not a circularity: no equation is equal by construction to another, no fitted parameter is renamed as a prediction, and the cited prior work is externally available and independently reproduced in the ablations. The limitation section's admission that GAIL hyperparameters vary per experiment further weakens generality, but again it does not make the derivation circular.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The framework does not introduce new physical entities. Its load-bearing ingredients are the hand-tuned reward scalers, the chosen perturbation models, the MuJoCo simulator as a stand-in for real dynamics, and the assumption that expert trajectories are suitable demonstrations. These are the assumptions a replication study would need to examine first.

free parameters (2)

reward scalers s1..s5 = s1=1, s2=0.5, s3=1, s4=9, s5=500
Hand-tuned weights in the reward function (Eq. 15) chosen from prior work and adjusted, e.g., s5 raised from 25 to 500. The central behavior of the expert depends on these values.
per-experiment GAIL hyperparameters = not fully stated in visible text
The limitation section notes current GAIL hyperparameters vary in different experiments; this is an additional hand-tuning burden and a free choice that affects the learner results.

assumptions (5)

standard math Rigid-body quaternion kinematics and Euler dynamics (Eqs. 6-7) describe the satellite motion.
Invoked in the Kinematics and Dynamics Simulation section; standard model for attitude dynamics.
domain assumption MuJoCo simulates the dynamics with sufficient fidelity, including stable quaternion normalization.
The method section states MuJoCo is used to numerically solve Eqs. 6-7; no comparison to other simulators or real data.
domain assumption The chosen perturbation models (Gaussian gyro noise, random-walk drift, deterministic torque scaling, fixed Euler-angle misalignment) represent unknown perturbations.
Defined in Perturbations Parameters; no validation against physical failure data or real actuator/sensor logs.
ad hoc to paper The handcrafted reward in Eq. 15 is an adequate proxy for the goal of orienting and stabilizing the antenna.
Reward terms and scalers are specific to this paper; the expert and learner behavior depends on them.
domain assumption The expert's recorded trajectories are sufficiently optimal and diverse to serve as demonstrations for GAIL.
Implicit in the imitation-learning setup; no analysis of demonstration coverage or optimality is provided.

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Cite this review

Pith. "Pith review of Imitation Learning for Satellite Attitude Control under Unknown Perturbations." pith.science (2026). https://pith.science/paper/QWEOO2Q4

@misc{pith2026250701161,
  author       = {Pith},
  title        = {Pith review of: Imitation Learning for Satellite Attitude Control under Unknown Perturbations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QWEOO2Q4}},
  note         = {Machine review of arXiv:2507.01161}
}

read the original abstract

This paper presents a novel satellite attitude control framework that integrates Soft Actor-Critic (SAC) reinforcement learning with Generative Adversarial Imitation Learning (GAIL) to achieve robust performance under various unknown perturbations. Traditional control techniques often rely on precise system models and are sensitive to parameter uncertainties and external perturbations. To overcome these limitations, we first develop a SAC-based expert controller that demonstrates improved resilience against actuator failures, sensor noise, and attitude misalignments, outperforming our previous results in several challenging scenarios. We then use GAIL to train a learner policy that imitates the expert's trajectories, thereby reducing training costs and improving generalization through expert demonstrations. Preliminary experiments under single and combined perturbations show that the SAC expert can rotate the antenna to a specified direction and keep the antenna orientation reliably stable in most of the listed perturbations. Additionally, the GAIL learner can imitate most of the features from the trajectories generated by the SAC expert. Comparative evaluations and ablation studies confirm the effectiveness of the SAC algorithm and reward shaping. The integration of GAIL further reduces sample complexity and demonstrates promising imitation capabilities, paving the way for more intelligent and autonomous spacecraft control systems.

Figures

Figures reproduced from arXiv: 2507.01161 by the authors.

**Figure 2.** The evaluation of the angle difference α in various initial conditions (Experiment: Baseline) [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** The evaluation of the angle difference α in various initial conditions (Experiment: Single Torque Failure) In [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

Figures from the paper (25 more)

**Figure 4.** Figure 4: The evaluation of the angle difference α in various initial conditions (Experiment: Torque Noises and Attitude Misalignment) For comparison, even though Hao et al.9 got similar results in [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

**Figure 5.** Figure 5: The evaluation of the angle difference α in various initial conditions (Experiment: Single Torque Failure and Constant Attitude Misalignment) value as the expert in Experiments 1, 8, 6, and 11, even higher value in experiments 5 and 10. For other Experiments, even tho…

**Figure 6.** Figure 6: The evaluation of the angle difference α in various initial conditions (Experiment: Two Torque Failures) For Experiment 8, as we can see in [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]

**Figure 7.** Figure 7: The evaluation of the angle difference α in various initial conditions (Experiment: Gyroscope Noise Error and Gyroscope Constant Error) RMS Duty Cycle Max (◦ ) Min (◦ ) Learner 13.0336 0.9583 103.1712 0.8776 Expert 9.7284 0.9838 103.1190 0.6873 [PITH_FULL_IMAGE:figur…

**Figure 8.** Figure 8: The evaluation of the angle difference α in various initial conditions (Experiment: Gyroscope Drift Errors) LIMITATION AND FUTURE WORK The proposed method opens new avenues in the domain of spacecraft attitude management, presenting a pathway toward more autonomous, e…

**Figure 9.** Figure 9: Mean reward value during the training process of the learner and the expert [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]

**Figure 10.** Figure 10: The evaluation of the angle difference α in various initial conditions (Experiment 1) [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]

**Figure 11.** Figure 11: The evaluation of the angle difference α in various initial conditions (Experiment 8) Removing the SAC Algorithm Here are the results ( [PITH_FULL_IMAGE:figures/full_fig_p018_11.png]

**Figure 12.** Figure 12: The evaluation of the angle difference α in various initial conditions (Experiment 2, 3, and 4) not rotate rapidly around the target position afterward. Using the DDPG algorithm, the agent can’t keep the antenna of the satellite within the threshold for the gyroscope…

**Figure 13.** Figure 13: The evaluation of the angle difference α in various initial conditions (Experiment 5, 6, and 7) situations falls within the threshold if we don’t refine the reward function. Removing the refined reward function, agents trained by the SAC algorithm only make the error…

**Figure 14.** Figure 14: The evaluation of the angle difference α in various initial conditions (Experiment 10 and 11) RMS Duty Cycle Max (◦ ) Min (◦ ) Learner in Experiment 10 9.6879 0.9754 110.4877 0.7383 Expert in Experiment 10 8.7578 0.9861 104.2707 0.3524 Learner in Experiment 11 18.291…

**Figure 15.** Figure 15: The evaluation of the angle difference α in various initial conditions (Experiment: Single Torque Failure in Hao’s9 work) [PITH_FULL_IMAGE:figures/full_fig_p023_15.png]

**Figure 16.** Figure 16: The evaluation of the angle difference α in various initial conditions (Experiment: Torque Noises and Attitude Misalignment in Hao’s9 work) 23 [PITH_FULL_IMAGE:figures/full_fig_p023_16.png]

**Figure 17.** Figure 17: The evaluation of the angle difference α in various initial conditions (Experiment: Single Torque Failure and Constant Attitude Misalignment in Hao’s9 work) 24 [PITH_FULL_IMAGE:figures/full_fig_p024_17.png]

**Figure 18.** Figure 18: The evaluation of the angle difference α in various initial conditions (Experiment: Two Torque Failures in Hao’s9 work) 25 [PITH_FULL_IMAGE:figures/full_fig_p025_18.png]

**Figure 19.** Figure 19: The evaluation of the angle difference α in various initial conditions (Experiment: Single Torque Failure with the DDPG Algorithm and the Refined Reward Function) [PITH_FULL_IMAGE:figures/full_fig_p026_19.png]

**Figure 20.** Figure 20: The evaluation of the angle difference α in various initial conditions (Experiment: Torque Noises and Attitude Misalignment with the DDPG Algorithm and the Refined Reward Function) 26 [PITH_FULL_IMAGE:figures/full_fig_p026_20.png]

**Figure 21.** Figure 21: The evaluation of the angle difference α in various initial conditions (Experiment: Single Torque Failure and Constant Attitude Misalignment with the DDPG Algorithm and the Refined Reward Function) 27 [PITH_FULL_IMAGE:figures/full_fig_p027_21.png]

**Figure 22.** Figure 22: The Evaluation of the Angular Difference [PITH_FULL_IMAGE:figures/full_fig_p028_22.png]

**Figure 23.** Figure 23: The evaluation of the angle difference α in various initial conditions (Experiment: Torque Noises and Attitude Misalignment with Previous Reward Function and SAC Algorithm) 28 [PITH_FULL_IMAGE:figures/full_fig_p028_23.png]

**Figure 24.** Figure 24: The evaluation of the angle difference α in various initial conditions (Experiment: Single Torque Failure with Previous Reward Function and SAC Algorithm) [PITH_FULL_IMAGE:figures/full_fig_p029_24.png]

**Figure 25.** Figure 25: The evaluation of the angle difference α in various initial conditions (Experiment: Torque Noises and Attitude Misalignment with Previous Reward Function and SAC Algorithm) 29 [PITH_FULL_IMAGE:figures/full_fig_p029_25.png]

**Figure 26.** Figure 26: The evaluation of the angle difference α in various initial conditions (Experiment: Single Torque Failure and Constant Attitude Misalignment with Previous Reward Function and SAC Algorithm) 30 [PITH_FULL_IMAGE:figures/full_fig_p030_26.png]

**Figure 27.** Figure 27: The evaluation of the angle difference α in various initial conditions (Experiment: Gyroscope Errors with Previous Reward Function and SAC Algorithm) 31 [PITH_FULL_IMAGE:figures/full_fig_p031_27.png]

**Figure 28.** Figure 28: Ablation Study for the GAIL Algorithm 32 [PITH_FULL_IMAGE:figures/full_fig_p032_28.png]

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Reference graph

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Pith tools

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

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Reorient Satellite Antenna using Reinforcement Learning under Unknown At- titude Failures,

H. Peng and X. Bai, “Reorient Satellite Antenna using Reinforcement Learning under Unknown At- titude Failures,” AIAA SciTech F orum and Exposition, 2023 , American Institute of Aeronautics and Astronautics Inc, AIAA, 2023

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