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We present NARUTO, a neural active reconstruction system that combines a hybrid neural representation with uncertainty learning, enabling high-fidelity surface reconstruction. Our approach leverages a multi-resolution hash-grid as the mapping backbone, chosen for its exceptional convergence speed and capacity to capture high-frequency local features.The centerpiece of our work is the incorporation of an uncertainty learning module that dynamically quantifies reconstruction uncertainty while actively reconstructing the environment. By harnessing learned uncertainty, we propose a novel uncertainty aggregation strategy for goal searching and efficient path planning. Our system autonomously explores by targeting uncertain observations and reconstructs environments with remarkable completeness and fidelity. We also demonstrate the utility of this uncertainty-aware approach by enhancing SOTA neural SLAM systems through an active ray sampling strategy. Extensive evaluations of NARUTO in various environments, using an indoor scene simulator, confirm its superior performance and state-of-the-art status in active reconstruction, as evidenced by its impressive results on benchmark datasets like Replica and MP3D., Comment: Accepted to CVPR2024. Project page: https://oppo-us-research.github.io/NARUTO-website/. Code: https://github.com/oppo-us-research/NARUTO

The development of semiconductor optoelectronic devices is moving toward low power consumption and miniaturization, especially for high-efficiency quantum emitters. However, most of these quantum sources work at low carrier density region, where the Shockley-Read-Hall recombination may dominant and seriously reduce the emission efficiency. In order to diminish the affection of carrier trapping and sustain a strong photoluminescence emission under low power pumping condition, we investigated on the influence of Suspending to monolayered tungsten diselenide, novel two-dimensional quantum material. Not only the PL intensity, but also the fundamental photoluminescence quantum yield has exhibited a huge, order-scale enhancement through suspending, even surprisingly, we found the PLQY improvement revealed far significantly under small pumping power and came out an exponential increase tendency toward even lower carrier density region. With its strong excitonic effect, suspended WSe_2 offers a solution to reduce carrier trapping and participate in non-radiative processes. Moreover, in the low-power range where SRH recombination dominates, suspended WSe_2 exhibited remarkably higher percentage of excitonic radiation compared to contacted WSe_2. Herein, we quantitatively demonstrate the significance of suspended WSe_2 monolayer at low carrier density region, highlighting its potential for developing compact, low-power quantum emitters in the future.

Empirical and theoretical works show that the input weights of two-layer neural networks, when initialized with small values, converge towards isolated orientations. This phenomenon, referred to as condensation, indicates that the gradient descent methods tend to spontaneously reduce the complexity of neural networks during the training process. In this work, we elucidate the mechanisms behind the condensation phenomena occurring in the training of three-layer neural networks and distinguish it from the training of two-layer neural networks. Through rigorous theoretical analysis, we establish the blow-up property of effective dynamics and present a sufficient condition for the occurrence of condensation, findings that are substantiated by experimental results. Additionally, we explore the association between condensation and the low-rank bias observed in deep matrix factorization.

Heat, Ventilation and Air Conditioning (HVAC) systems play a critical role in maintaining a comfortable thermal environment and cost approximately 40% of primary energy usage in the building sector. For smart energy management in buildings, usage patterns and their resulting profiles allow the improvement of control systems with prediction capabilities. However, for large-scale HVAC system management, it is difficult to construct a detailed model for each subsystem. In this paper, a new data-driven room temperature prediction model is proposed based on the k-means clustering method. The proposed data-driven temperature prediction approach extracts the system operation feature through historical data analysis and further simplifies the system-level model to improve generalization and computational efficiency. We evaluate the proposed approach in the real world. The results demonstrated that our approach can significantly reduce modeling time without reducing prediction accuracy., Comment: Accepted and will be published on IEEE PES GM 2024

This paper addresses an optimal guidance problem concerning the vertical landing of a lunar lander with the objective of minimizing fuel consumption. The vertical landing imposes a final attitude constraint, which is treated as a final control constraint. To handle this constraint, we propose a nonnegative small regularization term to augment the original cost functional. This ensures the satisfaction of the final control constraint in accordance with Pontryagin's Minimum Principle. By leveraging the necessary conditions for optimality, we establish a parameterized system that facilitates the generation of numerous optimal trajectories, which contain the nonlinear mapping from the flight state to the optimal guidance command. Subsequently, a neural network is trained to approximate such mapping. Finally, numerical examples are presented to validate the proposed method.

Scalar fields play an important role in constructing modified gravity theories. In the case of a single scalar field with timelike gradient, the corresponding Lagrangian in the unitary gauge takes the form of spatially covariant gravity (SCG), which is proved useful in analyzing and extending the generally covariant theories. In this work, we apply the SCG method to the scalar-nonmetricity theory, of which the Lagrangian is built of the nonmetricity tensor and a scalar field. We derive the 3+1 decomposition of the geometric quantities and especially covariant derivatives of the scalar field up to the third order in the presence of a nonvanishing nonmetricity tensor. By fixing the unitary gauge, the resulting Lagrangian takes the form of a SCG with nonmetricity, in which all the ingredients are spatial tensors. We then exhaust the scalar monomials of SCG with nonmetricity up to $d=3$ with $d$ the total number of derivatives. Since the disformation tensor plays as an auxiliary variable, we take the Lagrangian with $d=2$ as an example to show that after solving the disformation tensor, we can get an effective SCG theory for the metric variables but with modified coefficients. Our results provides a novel approach to extending the scalar-nonmetricity theory., Comment: 26 pages, no figure; v3: match epjc version

This work presents a Physics-Informed Indirect Method (PIIM) that propagates the dynamics of both states and co-states backward in time for trajectory optimization problems. In the case of a Time-Optimal Soft Landing Problem (TOSLP), based on the initial co-state vector normalization technique, we show that the initial guess of the mass co-state and the numerical factor can be eliminated from the shooting procedure. As a result, the initial guess of the unknown co-states can be constrained to lie on a unit 3-D hypersphere. Then, using the PIIM allows one to exploit the physical significance of the optimal control law, which further narrows down the solution space to a unit 3-D octant sphere. Meanwhile, the analytical estimations of the fuel consumption and final time are provided. Additionally, a usually overlooked issue that results in an infeasible solution with a negative final time, is fixed by a simple remedy strategy. Consequently, the reduced solution space becomes sufficiently small to ensure fast, robust, and guaranteed convergence for the TOSLP. Then, we extend the PIIM to solve the Fuel-Optimal Soft Landing Problem (FOSLP) with a homotopy approach. The numerical simulations show that compared with the conventional indirect method with a success rate of 89.35%, it takes a shorter time for the proposed method to find the feasible solution to the FOSLP with a success rate of 100%., Comment: This paper has been published by IEEE T-AES with doi:10.1109/TAES.2024.3438687

Consensus-based decentralized stochastic gradient descent (D-SGD) is a widely adopted algorithm for decentralized training of machine learning models across networked agents. A crucial part of D-SGD is the consensus-based model averaging, which heavily relies on information exchange and fusion among the nodes. Specifically, for consensus averaging over wireless networks, communication coordination is necessary to determine when and how a node can access the channel and transmit (or receive) information to (or from) its neighbors. In this work, we propose $\texttt{BASS}$, a broadcast-based subgraph sampling method designed to accelerate the convergence of D-SGD while considering the actual communication cost per iteration. $\texttt{BASS}$ creates a set of mixing matrix candidates that represent sparser subgraphs of the base topology. In each consensus iteration, one mixing matrix is sampled, leading to a specific scheduling decision that activates multiple collision-free subsets of nodes. The sampling occurs in a probabilistic manner, and the elements of the mixing matrices, along with their sampling probabilities, are jointly optimized. Simulation results demonstrate that $\texttt{BASS}$ enables faster convergence with fewer transmission slots compared to existing link-based scheduling methods. In conclusion, the inherent broadcasting nature of wireless channels offers intrinsic advantages in accelerating the convergence of decentralized optimization and learning., Comment: 11 pages, 5 figures, submitted for possible journal publication. arXiv admin note: text overlap with arXiv:2310.16106

With the rapidly expanded field of two-dimensional(2D) magnetic materials, the frustrated magnetic skyrmions are attracting growing interest recently. Here, based on hexagonal close-packed (HCP) lattice of $J_1$-$J_2$ Heisenberg spins model, we systematically investigate the frustrated skyrmions and phase transition by micromagnetic simulations and first-principles calculations. The results show that four spin phases of antiferromagnetic, labyrinth domain, skyrmion and ferromagnetic textures are determined by the identified ranges of $J_1$-$J_2$. Importantly, skyrmion phase with an increasing topological number ($Q$) covers a wider $J_1$-$J_2$ area. Then, the diameter of skyrmions can be tuned by the frustration strength ($|J_2/J_1|$) or external magnetic field. Besides, a phase transition from N$\acute{e}$el to Bloch type skyrmion is observed due to the change of the helicity with the variation of $|J_2/J_1|$. Furthermore, as increasing magnetic field, the skyrmions with high $Q$ ($\ge 3$) tend to split into the ones with $Q=1$, thereby achieving a lower systematic energy. Additionally, we find that the CoCl$_2$ monolayer satisfies the requirement of the frustrated $J_1$-$J_2$ magnet, and the related magnetic behaviors agree with the above conclusions. The frustration-induced skyrmions are stable without the manipulation of temperature and magnetic field. Our results may open a possible way toward spintronic applications based on High-topological-number and nanoscale topological spin textures of skyrmions., Comment: 7 pages, 5 figures

Spiking Neural Networks (SNNs) that operate in an event-driven manner and employ binary spike representation have recently emerged as promising candidates for energy-efficient computing. However, a cost bottleneck arises in obtaining high-performance SNNs: training a SNN model requires a large number of time steps in addition to the usual learning iterations, hence this limits their energy efficiency. This paper proposes a general training framework that enhances feature learning and activation efficiency within a limited time step, providing a new solution for more energy-efficient SNNs. Our framework allows SNN neurons to learn robust spike feature from different receptive fields and update neuron states by utilizing both current stimuli and recurrence information transmitted from other neurons. This setting continuously complements information within a single time step. Additionally, we propose a projection function to merge these two stimuli to smoothly optimize neuron weights (spike firing threshold and activation). We evaluate the proposal for both convolution and recurrent models. Our experimental results indicate state-of-the-art visual classification tasks, including CIFAR10, CIFAR100, and TinyImageNet.Our framework achieves 72.41% and 72.31% top-1 accuracy with only 1 time step on CIFAR100 for CNNs and RNNs, respectively. Our method reduces 10x and 3x joule energy than a standard ANN and SNN, respectively, on CIFAR10, without additional time steps., Comment: Accepted by ACML 2023

Fine-tuning has been demonstrated to be an effective method to improve the domain performance of large language models (LLMs). However, LLMs might fit the dataset bias and shortcuts for prediction, leading to poor generation performance. Previous works have proven that LLMs are prone to exhibit position bias, i.e., leveraging information positioned at the beginning or end, or specific positional cues within the input. Existing debiasing methods for LLMs require external bias knowledge or annotated non-biased samples, which is lacking for position debiasing and impractical in reality. In this work, we propose a self-supervised position debiasing (SOD) framework to mitigate position bias for LLMs. SOD leverages unsupervised responses from pre-trained LLMs for debiasing without relying on any external knowledge. To improve the quality of unsupervised responses, we propose an objective alignment (OAM) module to prune these responses. Experiments on eight datasets and five tasks show that SOD consistently outperforms existing methods in mitigating three types of position biases. Besides, SOD achieves this by sacrificing only a small performance on biased samples, which is general and effective. To facilitate the reproducibility of the results, we share the code of all methods and datasets on https://github.com/LZKSKY/SOD., Comment: Accepted by ACL 2024 findings, this is the camera-ready version; 21 pages, 22 figures

Identifying spatially complete planar primitives from visual data is a crucial task in computer vision. Prior methods are largely restricted to either 2D segment recovery or simplifying 3D structures, even with extensive plane annotations. We present PlanarNeRF, a novel framework capable of detecting dense 3D planes through online learning. Drawing upon the neural field representation, PlanarNeRF brings three major contributions. First, it enhances 3D plane detection with concurrent appearance and geometry knowledge. Second, a lightweight plane fitting module is proposed to estimate plane parameters. Third, a novel global memory bank structure with an update mechanism is introduced, ensuring consistent cross-frame correspondence. The flexible architecture of PlanarNeRF allows it to function in both 2D-supervised and self-supervised solutions, in each of which it can effectively learn from sparse training signals, significantly improving training efficiency. Through extensive experiments, we demonstrate the effectiveness of PlanarNeRF in various scenarios and remarkable improvement over existing works.

Over-the-Air (OtA) computation is a newly emerged concept for computing functions of data from distributed nodes by taking advantage of the wave superposition property of wireless channels. Despite its advantage in communication efficiency, OtA computation is associated with significant security and privacy concerns that have so far not been thoroughly investigated, especially in the case of active attacks. In this paper, we propose and evaluate a detection scheme against active attacks in OtA computation systems. More explicitly, we consider an active attacker which is an external node sending random or misleading data to alter the aggregated data received by the server. To detect the presence of the attacker, in every communication period, legitimate users send some dummy samples in addition to the real data. We propose a detector design that relies on the existence of a shared secret only known by the legitimate users and the server, that can be used to hide the transmitted signal in a secret subspace. After the server projects the received vector back to the original subspace, the dummy samples can be used to detect active attacks. We show that this design achieves good detection performance for a small cost in terms of channel resources., Comment: 6 pages, 4 figures, presented at 57:th Annual Asilomar Conference on Signals, Systems, and Computers, 2023

We present STADEE, a \textbf{STA}tistics-based \textbf{DEE}p detection method to identify machine-generated text, addressing the limitations of current methods that rely heavily on fine-tuning pre-trained language models (PLMs). STADEE integrates key statistical text features with a deep classifier, focusing on aspects like token probability and cumulative probability, crucial for handling nucleus sampling. Tested across diverse datasets and scenarios (in-domain, out-of-domain, and in-the-wild), STADEE demonstrates superior performance, achieving an 87.05% F1 score in-domain and outperforming both traditional statistical methods and fine-tuned PLMs, especially in out-of-domain and in-the-wild settings, highlighting its effectiveness and generalizability.

The nonvolatile magnetoresistive random access memory (MRAM) is believed to facilitate emerging applications, such as in memory computing, neuromorphic computing and stochastic computing. Two dimensional (2D) materials and their van der Waals heterostructures promote the development of MRAM technology, due to their atomically smooth interfaces and tunable physical properties. Here we report the all-2D magnetoresistive memories featuring all electrical data reading and writing at room temperature based on WTe2/Fe3GaTe2/BN/Fe3GaTe2 heterostructures. The data reading process relies on the tunnel magnetoresistance of Fe3GaTe2/BN/Fe3GaTe2. The data writing is achieved through current induced polarization of orbital magnetic moments in WTe2, which exert torques on Fe3GaTe2, known as the orbit transfer torque (OTT) effect. In contrast to the conventional reliance on spin moments in spin transfer torque and spin orbit torque, the OTT effect leverages the natural out of plane orbital moments, facilitating field-free perpendicular magnetization switching through interface currents. Our results indicate that the emerging OTT MRAM is promising for low power, high performance memory applications.

Image super-resolution (SR) methods typically model degradation to improve reconstruction accuracy in complex and unknown degradation scenarios. However, extracting degradation information from low-resolution images is challenging, which limits the model performance. To boost image SR performance, one feasible approach is to introduce additional priors. Inspired by advancements in multi-modal methods and text prompt image processing, we introduce text prompts to image SR to provide degradation priors. Specifically, we first design a text-image generation pipeline to integrate text into the SR dataset through the text degradation representation and degradation model. The text representation applies a discretization manner based on the binning method to describe the degradation abstractly. This method maintains the flexibility of the text and is user-friendly. Meanwhile, we propose the PromptSR to realize the text prompt SR. The PromptSR utilizes the pre-trained language model (e.g., T5 or CLIP) to enhance restoration. We train the PromptSR on the generated text-image dataset. Extensive experiments indicate that introducing text prompts into SR, yields excellent results on both synthetic and real-world images. Code is available at: https://github.com/zhengchen1999/PromptSR., Comment: Code is available at https://github.com/zhengchen1999/PromptSR

Patients with breast cancer tend to die from other diseases, so for studies that focus on breast cancer, a competing risks model is more appropriate. Considering subdistribution hazard ratio, which is used often, limited to model assumptions and clinical interpretation, we aimed to quantify the effects of prognostic factors by an absolute indicator, the difference in restricted mean time lost (RMTL), which is more intuitive. Additionally, prognostic factors may have dynamic effects (time-varying effects) in long-term follow-up. However, existing competing risks regression models only provide a static view of covariate effects, leading to a distorted assessment of the prognostic factor. To address this issue, we proposed a dynamic effect RMTL regression that can explore the between-group cumulative difference in mean life lost over a period of time and obtain the real-time effect by the speed of accumulation, as well as personalized predictions on a time scale. Through Monte Carlo simulation, we validated the dynamic effects estimated by the proposed regression having low bias and a coverage rate of around 95%. Applying this model to an elderly early-stage breast cancer cohort, we found that most factors had different patterns of dynamic effects, revealing meaningful physiological mechanisms underlying diseases. Moreover, from the perspective of prediction, the mean C-index in external validation reached 0.78. Dynamic effect RMTL regression can analyze both dynamic cumulative effects and real-time effects of covariates, providing a more comprehensive prognosis and better prediction when competing risks exist.

Computation of sample size is important when designing clinical trials. The presence of competing risks makes the design of clinical trials with time-to-event endpoints cumbersome. A model based on the subdistribution hazard ratio (SHR) is commonly used for trials under competing risks. However, this approach has some limitations related to model assumptions and clinical interpretation. Considering such limitations, the difference in restricted mean time lost (RMTLd) is recommended as an alternative indicator. In this paper, we propose a sample size calculation method based on the RMTLd for the Weibull distribution (RMTLdWeibull) for clinical trials, which considers experimental conditions such as equal allocation, uniform accrual, uniform loss to follow-up, and administrative censoring. Simulation results show that sample size calculation based on the RMTLdWeibull can generally achieve a predefined power level and maintain relative robustness. Moreover, the performance of the sample size calculation based on the RMTLdWeibull is similar or superior to that based on the SHR. Even if the event time does not follow the Weibull distribution, the sample size calculation based on the RMTLdWeibull still performs well. The results also verify the performance of the sample size calculation method based on the RMTLdWeibull. From the perspective of the results of this study, clinical interpretation, application conditions and statistical performance, we recommend that when designing clinical trials in the presence of competing risks, the RMTLd indicator be applied for sample size calculation and subsequent effect size measurement.

This paper is concerned with real-time generation of optimal flight trajectories for Minimum-Effort Control Problems (MECPs), which is fundamentally important for autonomous flight of aerospace vehicles. Although existing optimal control methods, such as indirect methods and direct methods, can be amended to solve MECPs, it is very challenging to obtain, in real time, the solution trajectories since those methods suffer the issue of convergence. As the artificial neural network can generate its output within a constant time, it has been alternative for real-time generation of optimal trajectories in the literature. The usual way is to train neural networks by solutions from indirect or direct methods, which, however, cannot ensure sufficient conditions for optimality to be met. As a result, the trained neural networks cannot be guaranteed to generate at least locally optimal trajectories. To address this issue, a parametrization approach is developed in the paper so that not only necessary but also sufficient conditions are embedded into a parameterized set of differential equations. This allows generating the data set of at least locally optimal trajectories through solving some initial value problems. Once a neural network is trained by the data set, it can not only generate optimal trajectories within milliseconds but also ensure the generated trajectories to be at least locally optimal, as finally demonstrated by two conventional MECPs in aerospace engineering.

The recently discovered AV$_{3}$Sb$_{5}$ (A = K, Rb, Cs) compounds have garnered intense attention in the scientific community due to their unique characteristics as kagome superconductors coexisting with a charge density wave (CDW) order. To comprehend the electronic properties of this system, it is essential to understand the lattice distortions associated with the CDW order and the ground state electronic behavior. Here, we comprehensively examine the Fermi surface by a combination of angle-dependent torque magnetometry and density functional theory calculations. We observe magnetic breakdown in the de Haas-van Alphen oscillations under high magnetic fields. Additionally, by examining the angular and temperature variations in quantum oscillation frequencies, we gain insight into the evolution of the three-dimensional like Fermi surfaces and the cyclotron masses of the orbits, which are consistent with weak electron-phonon coupling. Notably, further comparisons indicate that the 2$\times$2$\times$2 Star-of-David (SoD) distortion is more compatible with both high frequency data above 1000\,T and low frequency data below 500\,T, while the 2$\times$2$\times$2 Tri-Hexagonal (TrH) distortion aligns well with experimental data at mid frequencies. This finding implies the inherent coexistence of both TrH and SoD 2$\times$2$\times$2 patterns within the CDW order. These observations provide key insights into the interplay among effective electronic dimensionality, CDW state, and superconductivity.

Recent studies have demonstrated the great potential of Large Language Models (LLMs) serving as zero-shot relevance rankers. The typical approach involves making comparisons between pairs or lists of documents. Although effective, these listwise and pairwise methods are not efficient and also heavily rely on intricate prompt engineering. To tackle this problem, we introduce a novel instruction distillation method. The key idea is to distill the pairwise ranking ability of open-sourced LLMs to a simpler but more efficient pointwise ranking. Specifically, given the same LLM, we first rank documents using the effective pairwise approach with complex instructions, and then distill the teacher predictions to the pointwise approach with simpler instructions. Evaluation results on the BEIR, TREC, and ReDial datasets demonstrate that instruction distillation can improve efficiency by 10 to 100x and also enhance the ranking performance of LLMs. Furthermore, our approach surpasses the performance of existing supervised methods like monoT5 and is on par with the state-of-the-art zero-shot methods. The code to reproduce our results is available at www.github.com/sunnweiwei/RankGPT.

This work centers on the communication aspects of decentralized learning over wireless networks, using consensus-based decentralized stochastic gradient descent (D-SGD). Considering the actual communication cost or delay caused by in-network information exchange in an iterative process, our goal is to achieve fast convergence of the algorithm measured by improvement per transmission slot. We propose BASS, an efficient communication framework for D-SGD over wireless networks with broadcast transmission and probabilistic subgraph sampling. In each iteration, we activate multiple subsets of non-interfering nodes to broadcast model updates to their neighbors. These subsets are randomly activated over time, with probabilities reflecting their importance in network connectivity and subject to a communication cost constraint (e.g., the average number of transmission slots per iteration). During the consensus update step, only bi-directional links are effectively preserved to maintain communication symmetry. In comparison to existing link-based scheduling methods, the inherent broadcasting nature of wireless channels offers intrinsic advantages in speeding up convergence of decentralized learning by creating more communicated links with the same number of transmission slots., Comment: 6 pages, 4 figures, submitted for possible conference publication

Mapless navigation has emerged as a promising approach for enabling autonomous robots to navigate in environments where pre-existing maps may be inaccurate, outdated, or unavailable. In this work, we propose an image-based local representation of the environment immediately around a robot to parse navigability. We further develop a local planning and control framework, a Pareto-optimal mapless visual navigator (POVNav), to use this representation and enable autonomous navigation in various challenging and real-world environments. In POVNav, we choose a Pareto-optimal sub-goal in the image by evaluating all the navigable pixels, finding a safe visual path, and generating actions to follow the path using visual servo control. In addition to providing collision-free motion, our approach enables selective navigation behavior, such as restricting navigation to select terrain types, by only changing the navigability definition in the local representation. The ability of POVNav to navigate a robot to the goal using only a monocular camera without relying on a map makes it computationally light and easy to implement on various robotic platforms. Real-world experiments in diverse challenging environments, ranging from structured indoor environments to unstructured outdoor environments such as forest trails and roads after a heavy snowfall, using various image segmentation techniques demonstrate the remarkable efficacy of our proposed framework.

Over-the-Air (OtA) Federated Learning (FL) refers to an FL system where multiple agents apply OtA computation for transmitting model updates to a common edge server. Two important features of OtA computation, namely linear processing and signal-level superposition, motivate the use of linear compression with compressed sensing (CS) methods to reduce the number of data samples transmitted over the channel. The previous works on applying CS methods in OtA FL have primarily assumed that the original model update vectors are sparse, or they have been sparsified before compression. However, it is unclear whether linear compression with CS-based reconstruction is more effective than directly sending the non-zero elements in the sparsified update vectors, under the same total power constraint. In this study, we examine and compare several communication designs with or without sparsification. Our findings demonstrate that sparsification before compression is not necessary. Alternatively, sparsification without linear compression can also achieve better performance than the commonly considered setup that combines both., Comment: 6 pages, 8 figures, submitted for possible conference publication

This work is devoted to generating optimal guidance commands in real time for attitude-constrained solar sailcrafts in coplanar circular-to-circular interplanetary transfers. Firstly, a nonlinear optimal control problem is established, and necessary conditions for optimality are derived by the Pontryagin's Minimum Principle. Under some assumptions, the attitude constraints are rewritten as control constraints, which are replaced by a saturation function so that a parameterized system is formulated to generate an optimal trajectory via solving an initial value problem. This approach allows for the efficient generation of a dataset containing optimal samples, which are essential for training Neural Networks (NNs) to achieve real-time implementation. However, the optimal guidance command may suddenly change from one extreme to another, resulting in discontinuous jumps that generally impair the NN's approximation performance. To address this issue, we use two co-states that the optimal guidance command depends on, to detect discontinuous jumps. A procedure for preprocessing these jumps is then established, thereby ensuring that the preprocessed guidance command remains smooth. Meanwhile, the sign of one co-state is found to be sufficient to revert the preprocessed guidance command back into the original optimal guidance command. Furthermore, three NNs are built and trained offline, and they cooperate together to precisely generate the optimal guidance command in real time. Finally, numerical simulations are presented to demonstrate the developments of the paper.

Bang-bang control is ubiquitous for Optimal Control Problems (OCPs) where the constrained control variable appears linearly in the dynamics and cost function. Based on the Pontryagin's Minimum Principle, the indirect method is widely used to numerically solve OCPs because it enables to derive the theoretical structure of the optimal control. However, discontinuities in the bang-bang control structure may result in numerical difficulties for gradient-based indirect method. In this case, smoothing or regularization procedures are usually applied to eliminating the discontinuities of bang-bang controls. Traditional smoothing or regularization procedures generally modify the cost function by adding a term depending on a small parameter, or introducing a small error into the state equation. Those procedures may complexify the numerical algorithms or degenerate the convergence performance. To overcome these issues, we propose a bounded smooth function, called normalized L2-norm function, to approximate the sign function in terms of the switching function. The resulting optimal control is smooth and can be readily embedded into the indirect method. Then, the simplicity and improved performance of the proposed method over some existing methods are numerically demonstrated by a minimal-time oscillator problem and a minimal-fuel low-thrust trajectory optimization problem that involves many revolutions., Comment: This paper has been accpted for presentation at the 2024 AIAA Scitech