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26 pages, 1104 KB  
Article
Task Duration-Constrained Joint Resource Allocation and Trajectory Design for UAV-Assisted Backscatter Communication System
by Wenxin Zhou and Long Suo
Appl. Sci. 2026, 16(9), 4159; https://doi.org/10.3390/app16094159 - 23 Apr 2026
Viewed by 84
Abstract
Backscatter communication (BackCom) has emerged as an energy-efficient and low-cost communication paradigm, in which wireless devices transmit information by reflecting incident signals rather than actively generating radio frequency signals. Owing to the extremely low power consumption and hardware cost, BackCom is particularly suitable [...] Read more.
Backscatter communication (BackCom) has emerged as an energy-efficient and low-cost communication paradigm, in which wireless devices transmit information by reflecting incident signals rather than actively generating radio frequency signals. Owing to the extremely low power consumption and hardware cost, BackCom is particularly suitable for Internet of Things (IoT) devices with stringent low energy and cost constraints. However, due to the severe double channel attenuation inherent in backscatter links, conventional ground-based deployment of transmitters and receivers often suffers from poor communication quality and low energy efficiency. Unmanned aerial vehicles (UAVs), with their high mobility and favorable line-of-sight (LoS) links, can act as dynamic aerial transmitters and receivers in BackCom, thereby mitigating channel attenuation and improving both communication reliability and energy efficiency. To enhance the data collection efficiency of UAV-assisted BackCom systems under a limited mission duration, this paper proposes a joint optimization method for communication resource allocation and UAV trajectory design under task time constraints. Specifically, a mixed-integer non-convex optimization problem is formulated to maximize the number of devices served by the UAV within a given task duration. The original problem is then decomposed into two subproblems, namely communication resource allocation optimization and UAV trajectory optimization. An iterative algorithm based on Block Coordinate Descent (BCD) and Successive convex approximation (SCA) is developed to obtain an efficient solution. Simulation results demonstrate that the proposed method can effectively increase the number of served devices within the specified mission time limit. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
25 pages, 816 KB  
Article
Finite-Bit Distributed Optimization for UAV Swarms Under Communication Bandwidth Constraints
by Yingzheng Zhang and Zhenghong Jin
Symmetry 2026, 18(4), 676; https://doi.org/10.3390/sym18040676 - 18 Apr 2026
Viewed by 142
Abstract
This paper develops a unified finite-bit distributed optimization framework for UAV swarms operating over bandwidth-limited communication graphs. We consider strongly convex and smooth global objectives decomposed over local UAV cost functions and study three communication-efficient algorithmic regimes. First, we design a quantized distributed [...] Read more.
This paper develops a unified finite-bit distributed optimization framework for UAV swarms operating over bandwidth-limited communication graphs. We consider strongly convex and smooth global objectives decomposed over local UAV cost functions and study three communication-efficient algorithmic regimes. First, we design a quantized distributed gradient-tracking descent scheme with fixed finite-bit communication and show that, under bounded quantization errors, the method converges R-linearly to a quantization-dependent neighborhood of the global optimizer. Second, we introduce an adaptive quantization strategy that dynamically adjusts the number of transmitted bits according to the current convergence stage. By forcing the quantization distortion to decay proportionally to the optimization error, the proposed adaptive scheme recovers exact linear convergence to the optimal solution while substantially reducing the cumulative communication load. Third, we develop a fully distributed 1-bit communication mode in which UAVs exchange only sign information and use coordinate-wise majority voting to aggregate both descent and consensus directions. The robust linear-contraction property is proved to a small neighborhood under a sign-Polyak–Lojasiewicz condition and a probabilistic majority-correctness assumption. Full article
(This article belongs to the Section Computer)
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30 pages, 1668 KB  
Article
Joint Optimization for Energy Efficiency in UAV-Enabled Networks
by Cheru Haile Tesfay, Zheng Xiang, Long Yang, Jabar Mahmood, Shehzad Ashraf Chaudhry and Ashok Kumar Das
Drones 2026, 10(4), 262; https://doi.org/10.3390/drones10040262 - 4 Apr 2026
Viewed by 898
Abstract
Unmanned Aerial Vehicles (UAVs) were originally designed for military and surveillance applications but are now significant in smart agriculture, wireless communication, and product delivery. In contrast to an Internet Service Provider (ISP), which typically relies on fixed base stations, which can fail in [...] Read more.
Unmanned Aerial Vehicles (UAVs) were originally designed for military and surveillance applications but are now significant in smart agriculture, wireless communication, and product delivery. In contrast to an Internet Service Provider (ISP), which typically relies on fixed base stations, which can fail in the event of a disaster, UAVs offer more stable alternatives. Because IoT devices, sensors, and ground users have limited processing power and battery life, there is a need for energy-efficient solutions. Meanwhile, users still expect high data rates. UAV-based wireless networks can meet these needs, even in harsh or disaster-hit areas. Current research focuses on improving energy efficiency and data transmission by optimizing UAV flight paths and scheduling. In this work, we tackle these issues by formulating a mixed-integer non-convex optimization problem that jointly considers device scheduling and UAV trajectory. We further decompose it into the following two parts: energy-efficient scheduling among ground users (P2) and the trajectory optimization of UAVs (P3). To address these issues, we develop a linear programming relaxation approach, a Quadratically Constrained Quadratic Programming (QCQP)-based Successive Convex Approximation (SCA) scheme, and the Block Coordinate Descent (BCD) algorithm. Experimental results demonstrate that our approach outperforms the state of the art in both power consumption and transmission rate. Full article
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29 pages, 10526 KB  
Article
A Distributed Stochastic Optimization Scheduling Method Using Diffusion-TS Generated Scenario for Integrated Energy System
by Panpan Xia, Chen Chen, Li Sun and Lei Pan
Energies 2026, 19(7), 1763; https://doi.org/10.3390/en19071763 - 3 Apr 2026
Viewed by 388
Abstract
The optimal dispatch of integrated energy systems (IESs) is strongly affected by uncertainties on both the supply and demand sides. To model wind power uncertainty and embed it into dispatch decision-making, this paper develops a distributed stochastic scheduling method driven by Diffusion-TS-based scenario [...] Read more.
The optimal dispatch of integrated energy systems (IESs) is strongly affected by uncertainties on both the supply and demand sides. To model wind power uncertainty and embed it into dispatch decision-making, this paper develops a distributed stochastic scheduling method driven by Diffusion-TS-based scenario generation. First, a conditional Diffusion-TS model is developed to generate high-fidelity wind power scenarios from day-ahead forecasts, and a temperature parameter is introduced to balance scenario diversity and fidelity. Second, a distributed stochastic scheduling framework with chance constraints is established, in which the probabilistic constraints are reformulated into a mixed-integer linear programming problem to address source-load fluctuations while preserving subsystem privacy. Third, the block coordinate descent method is used to decompose the system into cooling, heating, and electricity subproblems for iterative solution. Case study results show that the average CRPS of the generated scenarios is 162.16 MW, which is 34% lower than that of the deterministic forecast benchmark. The total cost of distributed deterministic dispatch is 2.8% higher than that of centralized deterministic dispatch, while the total cost of distributed stochastic dispatch is 53.1% higher than that of distributed deterministic dispatch, reflecting the additional economic cost of uncertainty-aware scheduling. Compared with the traditional LHS-Kmeans method, the scenarios generated by Diffusion-TS are closer to the actual wind power output. Although the resulting dispatch cost is higher, the obtained scheduling results are more consistent with realistic wind power conditions. Overall, the proposed method provides a practical technical route for the secure and economical operation of IESs under uncertainty. Full article
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18 pages, 1279 KB  
Article
Distributed and Data-Driven Optimization Frameworks for Logistics-Oriented Decision Support Under Partial and Asynchronous Information
by Manuel J. C. S. Reis
Algorithms 2026, 19(4), 246; https://doi.org/10.3390/a19040246 - 24 Mar 2026
Viewed by 190
Abstract
This paper introduces D3O-GT, a distributed optimization framework designed to operate under partial, heterogeneous, and delayed information—conditions commonly encountered in large-scale logistics and networked decision support systems. The proposed approach integrates gradient tracking with delay-aware updates to address the steady-state bias [...] Read more.
This paper introduces D3O-GT, a distributed optimization framework designed to operate under partial, heterogeneous, and delayed information—conditions commonly encountered in large-scale logistics and networked decision support systems. The proposed approach integrates gradient tracking with delay-aware updates to address the steady-state bias and instability that often affect classical distributed gradient methods. We formulate a consensus optimization model that captures decentralized decision variables while preserving global optimality, and we develop an algorithmic structure that balances convergence accuracy, communication efficiency, and robustness to asynchronous updates. Extensive numerical experiments demonstrate that D3O-GT achieves machine precision convergence in synchronous settings and remains stable under bounded communication delays, converging to a small neighborhood of the optimum. In contrast, conventional distributed gradient descent exhibits significant residual error under the same conditions. Scalability analyses further indicate that the proposed method maintains favorable iteration complexity as the number of agents increases. These results position D3O-GT as a practical and scalable solution for distributed decision-making environments, with direct relevance to logistics-oriented applications such as resource allocation, coordination of networked services, and real-time operational planning. Full article
(This article belongs to the Special Issue Optimizing Logistics Activities: Models and Applications)
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29 pages, 3179 KB  
Article
A Convex Optimization Framework for 6-DOF Lunar Powered Descent with a Normalized Finite Rotation Parameterization
by Yandi Qiao and Zexu Zhang
Aerospace 2026, 13(4), 300; https://doi.org/10.3390/aerospace13040300 - 24 Mar 2026
Viewed by 325
Abstract
There has been increasing interest in the Moon for deep space exploration missions in the last few decades. To accommodate fuel-optimal lunar landing missions, it is essential to develop a fast trajectory planning algorithm considering constrained six-degree-of-freedom (6-DOF) dynamics. On the one hand, [...] Read more.
There has been increasing interest in the Moon for deep space exploration missions in the last few decades. To accommodate fuel-optimal lunar landing missions, it is essential to develop a fast trajectory planning algorithm considering constrained six-degree-of-freedom (6-DOF) dynamics. On the one hand, the trajectory planning problem involves a coordination of the optimal fuel consumption and the vehicle’s position, velocity, and attitude, which requires computational efficiency. On the other hand, the initialization setup of the existing sequential convex optimization method provides the linear reference trajectory, which slows down the convergence of the iterative process. In this manuscript, an improved sequential convex programming algorithm is proposed to solve the minimum-fuel 6-DOF powered descent problem. Firstly, we suggest a trajectory planning method based on a normalized finite rotation formulation, which improves the efficiency of the computational processes. Secondly, we present an initial guess method that computes the projection-analogous gradient with respect to the terminal value, accelerating the convergence of the algorithm. The simulation results show that the proposed method improves computational efficiency, indicating the potential for future applications in autonomous landing missions. Full article
(This article belongs to the Special Issue Intelligent Multi-Agent Systems for Advanced Space Applications)
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18 pages, 8749 KB  
Article
Biomechanical and Signal-Based Characterization of Karate Lateral Kicks Using Videogrammetry Analysis
by Luis Antonio Aguilar-Pérez, Jorge Luis Rojas-Arce, Luis Jímenez-Ángeles, Carlos Alberto Espinoza-Garces, Adolfo Ángel Casarez-Duran and Christopher René Torres-SanMiguel
Machines 2026, 14(3), 339; https://doi.org/10.3390/machines14030339 - 17 Mar 2026
Viewed by 527
Abstract
Martial arts have evolved from self-defense practices into structured competitive sports that demand high levels of neuromotor control, where improper execution remains a major source of injury. This study evaluates lower-limb control during the execution of the karate lateral kick using videogrammetry biomechanical [...] Read more.
Martial arts have evolved from self-defense practices into structured competitive sports that demand high levels of neuromotor control, where improper execution remains a major source of injury. This study evaluates lower-limb control during the execution of the karate lateral kick using videogrammetry biomechanical analysis. Three participants were recorded during regular training sessions and selected according to their level of expertise. Each participant performed lateral kicks at three predefined distances (close, comfortable, and long), selected based on common training practice and individual biomechanical considerations. Videogrammetry data were generated using Kinovea version 0.9.5 software to extract sagittal ankle trajectories. Statistical analyses were carried out in MATLAB version 2025b using spatial coordinates to obtain kinematic data on the practitioner’s performance. The results revealed skill-dependent differences in movement control, characterized by temporal evolution of kinematic variables and their corresponding time–frequency representations. Novice practitioners exhibited limited control during the raising and recovery phases, despite reaching the target. In contrast, expert practitioners demonstrated consistent posture, controlled acceleration during impact, and stable limb trajectories during descent. These observations provide a foundation for data-driven classification of kick execution quality and outline potential applications in supervised learning, real-time feedback systems, and injury risk reduction during karate training. Full article
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27 pages, 9034 KB  
Article
A Comparison of Optimisation Algorithms for Electronic Polarisation Control in Quantum Key Distribution
by Matt Young, Haofan Duan, Stefano Pirandola and Marco Lucamarini
Appl. Sci. 2026, 16(5), 2568; https://doi.org/10.3390/app16052568 - 7 Mar 2026
Viewed by 420
Abstract
Polarisation encoding is widely used in fibre-based Quantum Key Distribution (QKD), but random birefringence in optical fibres causes the transmitted states to drift, requiring active compensation at the receiver. Electronic Polarisation Controllers (EPCs) are commonly used for this purpose, yet the relationship between [...] Read more.
Polarisation encoding is widely used in fibre-based Quantum Key Distribution (QKD), but random birefringence in optical fibres causes the transmitted states to drift, requiring active compensation at the receiver. Electronic Polarisation Controllers (EPCs) are commonly used for this purpose, yet the relationship between their control voltages and the resulting polarisation transformation is highly nonlinear and difficult to model. While optimisation algorithms are frequently employed to align and stabilise polarisation states, their comparative performance has not been systematically studied in realistic QKD settings. In this work, we benchmark four optimisation algorithms for electronic polarisation control, using both a numerical model and a 50 km fibre-based experimental setup. We evaluate each algorithm in terms of convergence time, failure rate, and stability, under both initial alignment and continuous drift compensation scenarios. Coordinate Descent achieved the fastest average alignment time (2.1 ms in simulation; 34.6 s experimentally), while Simulated Annealing delivered perfect reliability. We further propose a hybrid control strategy that combines fast initial alignment with high-reliability realignment. This approach was validated over a continuous 2 h QKD simulation with real fibre drift, demonstrating robust polarisation control without manual intervention. Our results provide guidance for algorithm selection in practical QKD deployments and suggest a pathway to resilient, autonomous polarisation tracking in long-distance quantum networks. Full article
(This article belongs to the Special Issue Quantum Communication and Quantum Information)
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22 pages, 824 KB  
Article
Security Improvement for UAV-Assisted Integrated Sensing, Communication, and Jamming Networks
by Lin Shi, Chuansheng Yan, Dingcheng Yang, Yu Xu, Fahui Wu and Huabing Lu
Telecom 2026, 7(2), 27; https://doi.org/10.3390/telecom7020027 - 3 Mar 2026
Viewed by 606
Abstract
We propose a unmanned aerial vehicle (UAV)-assisted integrated sensing, communication, and jamming (U-ISJC) framework, in which a multifunctional UAV first detects the sensing target to obtain sensing information, and subsequently transmits the information to communication users via a unified beam in the presence [...] Read more.
We propose a unmanned aerial vehicle (UAV)-assisted integrated sensing, communication, and jamming (U-ISJC) framework, in which a multifunctional UAV first detects the sensing target to obtain sensing information, and subsequently transmits the information to communication users via a unified beam in the presence of multiple eavesdroppers. To avoid functional conflicts, a time slot frame structure is designed for the UAV’s multifunctional capabilities, enabling communication, sensing, and jamming tasks within each timeslot. The time slot allocation factor dynamically adjusts based on the UAV’s flight trajectory for efficient UAV resource utilization. Additionally, to prevent security rate leakage caused by eavesdroppers, a jamming beam is added to serve both jamming and sensing functions. Our objective is to maximize the the worst-case total secure data transmission rate by jointly optimizing sub-time slot allocation, beamforming, and UAV trajectory. To address this problem, we propose a joint optimization algorithm that adopts the concave–convex procedure (CCCP) technique and semi-definite relaxation (SDR), under the block coordinate descent (BCD) framework. The simulation results show that compared with the baseline scheme, the proposed algorithm substantially improves the communication security rate while ensuring the quality of communication and sensing. Full article
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35 pages, 20162 KB  
Article
An Efficient and Sparse Kernelized Grey RVFL Network for Energy Forecasting
by Wenkang Gong and Gaofeng Zong
Systems 2026, 14(3), 257; https://doi.org/10.3390/systems14030257 - 28 Feb 2026
Viewed by 290
Abstract
Reliable energy forecasting is essential for the planning and dispatch of power and fuel systems; however, energy series are often short and exhibit pronounced nonlinearity. To tackle this small sample setting, we propose a gray random vector functional link (GRVFL) framework and further [...] Read more.
Reliable energy forecasting is essential for the planning and dispatch of power and fuel systems; however, energy series are often short and exhibit pronounced nonlinearity. To tackle this small sample setting, we propose a gray random vector functional link (GRVFL) framework and further derive a kernelized variant (KGRVFL). In GRVFL, an RVFL network is integrated into gray system modeling, and the parameters are learned via sparsity-regularized regression, enabling stable and reproducible training without backpropagation or evolutionary optimization. Hyperparameters are tuned using Bayesian optimization driven by a Top-k mean absolute percentage error (Top-k MAPE) criterion to improve robustness. To further promote compactness, we introduce a fractional ratio-type Fr-1 penalty and solve the resulting problem efficiently using a fractional coordinate descent (FCD) algorithm. The proposed methods are assessed on six real-world energy datasets using eight evaluation metrics. Comparisons with nine gray model baselines and six machine learning forecasters demonstrate that the sparse KGRVFL (SKGRVFL) achieves higher predictive accuracy and improved training stability under small sample conditions. Full article
(This article belongs to the Section Systems Engineering)
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23 pages, 1203 KB  
Article
A Bayesian Hierarchical Cox Model with Elastic Net Regularization for Improved Survival Prediction and Feature Selection
by Bulus I. Doroh, Kazeem A. Dauda and Rasheed K. Lamidi
Mathematics 2026, 14(5), 767; https://doi.org/10.3390/math14050767 - 25 Feb 2026
Viewed by 445
Abstract
In recent years, the growing availability of large-scale data across a wide range of disciplines has created new opportunities for developing models that improve the predictive accuracy of statistical models. Although techniques such as regularization and Bayesian hierarchical methods are commonly used for [...] Read more.
In recent years, the growing availability of large-scale data across a wide range of disciplines has created new opportunities for developing models that improve the predictive accuracy of statistical models. Although techniques such as regularization and Bayesian hierarchical methods are commonly used for building predictive models, substantial challenges remain, particularly when dealing with high-dimensional datasets that contain considerable noise. In this study, we propose a Bayesian hierarchical model that employs a spike-and-slab hierarchical elastic net prior that regularizes the Cox Proportional Hazards (Cox-PH) model. The method combines Bayesian modeling with the regularized partial log-likelihood of the Cox-PH framework, incorporating an Elastic Net penalty to estimate the joint posterior distribution under a hierarchical elastic net prior. We compute this posterior using an Expectation–Maximization Cyclic Coordinate Descent Algorithm (EM-CCDA), which streamlines feature selection and enhances overall predictive performance. We evaluate the algorithm’s performance through Monte Carlo simulations and apply it to three real-world datasets, comparing the results with those from established classical and Bayesian survival analysis approaches. The findings demonstrate notable gains in both feature selection and predictive accuracy, highlighting the model’s strong ability to predict patient survival and identify relevant genes in real biological datasets. Full article
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23 pages, 1454 KB  
Article
Energy-Efficient 3D Trajectory Optimization and Resource Allocation for UAV-Enabled ISAC Systems
by Lulu Jing, Hai Wang, Zhen Qin, Yicheng Zhao, Yi Zhu and Wensheng Zhao
Entropy 2026, 28(2), 248; https://doi.org/10.3390/e28020248 - 21 Feb 2026
Cited by 1 | Viewed by 434
Abstract
Owing to their high flexibility, autonomous operation, and rapid deployment capability, unmanned aerial vehicles (UAVs) serve as effective aerial platforms for sensing and communication in remote and time-critical scenarios. However, their limited onboard energy budget poses a significant bottleneck for sustained operations. This [...] Read more.
Owing to their high flexibility, autonomous operation, and rapid deployment capability, unmanned aerial vehicles (UAVs) serve as effective aerial platforms for sensing and communication in remote and time-critical scenarios. However, their limited onboard energy budget poses a significant bottleneck for sustained operations. This paper investigates an energy-efficient UAV-assisted integrated sensing and communication (ISAC) system, aiming to maximize the sensing energy efficiency (SEE), defined as the ratio of the total radar estimation rate to the total energy consumption. Unlike prior works focused solely on rate maximization or fairness, our design jointly optimizes the UAV’s 3D trajectory, task scheduling, and power allocation under kinematic and coverage constraints to maximize the SEE. To solve the formulated non-convex fractional programming problem, we propose an efficient iterative algorithm based on the Dinkelbach method and block coordinate descent (BCD). Simulation results demonstrate that the proposed scheme achieves a superior trade-off between sensing performance and energy consumption. Full article
(This article belongs to the Special Issue Integrated Sensing and Communication (ISAC) in 6G)
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19 pages, 4367 KB  
Article
A Neuro-Symbolic Approach to Fall Detection via Monocular Depth Estimation
by Yinghai Xu, Bongjun Kim, In-Nea Wang and Junho Jeong
Appl. Sci. 2026, 16(4), 1895; https://doi.org/10.3390/app16041895 - 13 Feb 2026
Viewed by 428
Abstract
Falls remain a critical safety concern in surveillance settings, yet monocular RGB methods often degrade in multi-person scenes with occlusion and loss of three-dimensional cues. This study proposes a neuro-symbolic framework that restores physically interpretable depth proxies from monocular video and fuses them [...] Read more.
Falls remain a critical safety concern in surveillance settings, yet monocular RGB methods often degrade in multi-person scenes with occlusion and loss of three-dimensional cues. This study proposes a neuro-symbolic framework that restores physically interpretable depth proxies from monocular video and fuses them with skeleton-based spatio-temporal inference for robust fall detection. The pipeline estimates per-frame depth and 2D skeletons, recovers world coordinates for key joints, and derives absolute neck height and vertical descent rate for rule-based adjudication, while a neural method operates on joint trajectories; final decisions combine both streams with a logical policy and short-horizon temporal consistency. Experiments in a realistic indoor testbed with multi-person activity compare three configurations—neural, symbolic, and fused. The fused neuro-symbolic method achieved an accuracy of 0.88 and an F1 score of 0.76 on the real surveillance test set, outperforming the neural method alone (accuracy 0.81, F1 0.64) and the symbolic method alone (accuracy 0.77, F1 0.35). Gains arise from complementary error profiles: depth-derived, rule-based cues suppress spurious positives on non-fall frames, while the neural stream recovers true falls near rule boundaries. These findings indicate that integrating monocular depth proxies with interpretable rules improves reliability without additional sensors, supporting deployment in complex, multi-person surveillance environments. Full article
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29 pages, 2638 KB  
Article
Satellite-Maritime Communication Network Based on RSMA and RIS: Sum Rate Maximization and Transmission Time Minimization
by Ying Zhang, Yuandi Zhao, Yongkang Chen, Weixiang Zhou, Zhihua Hu, Xinqiang Chen and Guowei Chen
J. Mar. Sci. Eng. 2026, 14(4), 342; https://doi.org/10.3390/jmse14040342 - 10 Feb 2026
Viewed by 472
Abstract
The maritime wireless communication network (MWCN) faces challenges such as limited coverage, inaccurate channel state information (CSI), and the sparse distribution of maritime vessel users. To overcome the above challenges, this paper proposes a low Earth orbit satellite (LEO) MWCN based on rate-splitting [...] Read more.
The maritime wireless communication network (MWCN) faces challenges such as limited coverage, inaccurate channel state information (CSI), and the sparse distribution of maritime vessel users. To overcome the above challenges, this paper proposes a low Earth orbit satellite (LEO) MWCN based on rate-splitting multiple access (RSMA) and reconfigurable intelligent surface (RIS). Common data streams transmit broadcast-shared information to all vessel users. Private data streams provide differentiated supplements. The primary optimization objective is to maximize the sum rate. The transmission time is also introduced as a supplementary performance indicator to assess the system’s transmission capability. To overcome the problems of imperfect CSI and the low efficiency of the weighted minimum mean square error (WMMSE) algorithm, a block coordinate descent (BCD) algorithm is proposed based on the deep unfolding method (DU) and momentum-accelerated projection gradient descent (PGD). Numerical results show that DU-WMMSE reduces the number of convergence iterations from 8 to 4, improves the sum rate by 11.06%, and achieves lower transmission time. In addition, active RIS mitigates severe fading more effectively in complex channels. The proposed scheme also exhibits excellent scalability. Full article
(This article belongs to the Section Ocean Engineering)
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25 pages, 2112 KB  
Article
Nabla Fractional Distributed Nash Equilibrium Seeking for Aggregative Games Under Partial-Decision Information
by Yao Xiao, Sunming Ge, Yihao Qiao, Tieqiang Gang and Lijie Chen
Fractal Fract. 2026, 10(2), 79; https://doi.org/10.3390/fractalfract10020079 - 24 Jan 2026
Viewed by 402
Abstract
For the first time, this paper introduces Nabla fractional calculus into the distributed Nash equilibrium (NE) seeking problem of aggregative games (AGs) with partial decision information in undirected communication networks, and proposes two novel fractional-order distributed algorithms. In the considered setting, each agent [...] Read more.
For the first time, this paper introduces Nabla fractional calculus into the distributed Nash equilibrium (NE) seeking problem of aggregative games (AGs) with partial decision information in undirected communication networks, and proposes two novel fractional-order distributed algorithms. In the considered setting, each agent can access to only local information and collaboratively estimates the global aggregate through communication with its neighbors. Both algorithms adopt a backward-difference scheme followed by an implicit fractional-order gradient descent step. One updates local aggregate estimates via fractional-order dynamic tracking and the other uses fractional-order average dynamic consensus protocols. Under standard assumptions, convergence of both algorithms to the NE is rigorously proved using nabla fractional-order Lyapunov stability theory, achieving a Mittag-Leffler convergence rate. The feasibility of the developed schemes is verified via numerical experiments applied to a Nash-Cournot game and the coordination control of flexible robotic arms. Full article
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