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Search Results (1,516)

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Keywords = Markov Systems

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25 pages, 874 KiB  
Article
Optimization Method for Reliability–Redundancy Allocation Problem in Large Hybrid Binary Systems
by Florin Leon and Petru Cașcaval
Mathematics 2025, 13(15), 2450; https://doi.org/10.3390/math13152450 - 29 Jul 2025
Viewed by 186
Abstract
This paper addresses a well-known research topic in the design of complex systems, specifically within the class of reliability optimization problems (ROPs). It focuses on optimal reliability–redundancy allocation problems (RRAPs) for large binary systems with hybrid structures. Two main objectives are considered: (1) [...] Read more.
This paper addresses a well-known research topic in the design of complex systems, specifically within the class of reliability optimization problems (ROPs). It focuses on optimal reliability–redundancy allocation problems (RRAPs) for large binary systems with hybrid structures. Two main objectives are considered: (1) to maximize system reliability under cost and volume constraints, and (2) to achieve the required reliability at minimal cost under a volume constraint. The system reliability model includes components with only two states: normal operating or failed. High reliability can result from directly improving component reliability, allocating redundancy, or using both approaches together. Several redundancy strategies are covered: active, passive, hybrid standby with hot, warm, or cold spares, static redundancy such as TMR and 5MR, TMR structures with control logic and spares, and reconfigurable TMR/Simplex structures. The proposed method uses a zero–one integer programming formulation that applies log-transformed reliability functions and binary decision variables to represent subsystem configurations. The experimental results validate the approach and confirm its efficiency. Full article
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14 pages, 1957 KiB  
Article
Reliability and Availability Analysis of a Two-Unit Cold Standby System with Imperfect Switching
by Nariman M. Ragheb, Emad Solouma, Abdullah A. Alahmari and Sayed Saber
Axioms 2025, 14(8), 589; https://doi.org/10.3390/axioms14080589 - 29 Jul 2025
Viewed by 109
Abstract
This paper presents a stochastic analysis of a two-unit cold standby system incorporating imperfect switching mechanisms. Each unit operates in one of three states: normal, partial failure, or total failure. Employing Markov processes, the study evaluates system reliability by examining the mean time [...] Read more.
This paper presents a stochastic analysis of a two-unit cold standby system incorporating imperfect switching mechanisms. Each unit operates in one of three states: normal, partial failure, or total failure. Employing Markov processes, the study evaluates system reliability by examining the mean time to failure (MTTF) and steady-state availability metrics. Failure and repair times are assumed to follow exponential distributions, while the switching mechanism is modeled as either perfect or imperfect. The results highlight the significant influence of switching reliability on both MTTF and system availability. This analysis is crucial for optimizing the performance of complex systems, such as thermal power plants, where continuous and reliable operation is imperative. The study also aligns with recent research trends emphasizing the integration of preventive maintenance and advanced reliability modeling approaches to enhance overall system resilience. Full article
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25 pages, 674 KiB  
Article
Sensor Fault Detection and Reliable Control of Singular Stochastic Systems with Time-Varying Delays
by Yunling Shi, Haosen Yang, Gang Liu, Xiaolin He and Jajun Wang
Sensors 2025, 25(15), 4667; https://doi.org/10.3390/s25154667 - 28 Jul 2025
Viewed by 130
Abstract
In unmanned systems, especially in large-scale and complex ones, sensor and communication failures occur from time to time and are hard to avoid. Therefore, this paper studies the fault detection problem of a class of unknown nonlinear singular uncertain time-varying delay Markov jump [...] Read more.
In unmanned systems, especially in large-scale and complex ones, sensor and communication failures occur from time to time and are hard to avoid. Therefore, this paper studies the fault detection problem of a class of unknown nonlinear singular uncertain time-varying delay Markov jump systems (UNSUTVDMJSs). Firstly, the corresponding sliding mode controller (SMC) is designed by using the equivalent control principle, and the unknown nonlinearity is equivalently replaced by changing the system input. Then, a fault detection filter adapted to this system is designed, thereby obtaining the unknown nonlinear stochastic singular uncertain Augmented filter residual system (UNSSUAFRS) model. To obtain the sufficient conditions for the random admissibility of this augmented system, a weak infinitesimal generator was used to design the required Lyapunov-Krasovskii functional. With the help of the Lyapunov principle and H performance analysis method, the sufficient conditions for the random admissibility of UNSSUAFRS under the H performance index γ were derived. Finally, with the aid of the designed residual evaluation function and threshold, simulation analysis was conducted on the examples of DC servo motors and numerical calculation examples to verify the effectiveness and practicability of this fault detection filter. Full article
(This article belongs to the Special Issue Smart Sensing and Control for Autonomous Intelligent Unmanned Systems)
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21 pages, 4738 KiB  
Article
Research on Computation Offloading and Resource Allocation Strategy Based on MADDPG for Integrated Space–Air–Marine Network
by Haixiang Gao
Entropy 2025, 27(8), 803; https://doi.org/10.3390/e27080803 - 28 Jul 2025
Viewed by 193
Abstract
This paper investigates the problem of computation offloading and resource allocation in an integrated space–air–sea network based on unmanned aerial vehicle (UAV) and low Earth orbit (LEO) satellites supporting Maritime Internet of Things (M-IoT) devices. Considering the complex, dynamic environment comprising M-IoT devices, [...] Read more.
This paper investigates the problem of computation offloading and resource allocation in an integrated space–air–sea network based on unmanned aerial vehicle (UAV) and low Earth orbit (LEO) satellites supporting Maritime Internet of Things (M-IoT) devices. Considering the complex, dynamic environment comprising M-IoT devices, UAVs and LEO satellites, traditional optimization methods encounter significant limitations due to non-convexity and the combinatorial explosion in possible solutions. A multi-agent deep deterministic policy gradient (MADDPG)-based optimization algorithm is proposed to address these challenges. This algorithm is designed to minimize the total system costs, balancing energy consumption and latency through partial task offloading within a cloud–edge-device collaborative mobile edge computing (MEC) system. A comprehensive system model is proposed, with the problem formulated as a partially observable Markov decision process (POMDP) that integrates association control, power control, computing resource allocation, and task distribution. Each M-IoT device and UAV acts as an intelligent agent, collaboratively learning the optimal offloading strategies through a centralized training and decentralized execution framework inherent in the MADDPG. The numerical simulations validate the effectiveness of the proposed MADDPG-based approach, which demonstrates rapid convergence and significantly outperforms baseline methods, and indicate that the proposed MADDPG-based algorithm reduces the total system cost by 15–60% specifically. Full article
(This article belongs to the Special Issue Space-Air-Ground-Sea Integrated Communication Networks)
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25 pages, 3791 KiB  
Article
Optimizing Multitenancy: Adaptive Resource Allocation in Serverless Cloud Environments Using Reinforcement Learning
by Mohammed Naif Alatawi
Electronics 2025, 14(15), 3004; https://doi.org/10.3390/electronics14153004 - 28 Jul 2025
Viewed by 101
Abstract
The growing adoption of serverless computing has highlighted critical challenges in resource allocation, policy fairness, and energy efficiency within multitenancy cloud environments. This research proposes a reinforcement learning (RL)-based adaptive resource allocation framework to address these issues. The framework models resource allocation as [...] Read more.
The growing adoption of serverless computing has highlighted critical challenges in resource allocation, policy fairness, and energy efficiency within multitenancy cloud environments. This research proposes a reinforcement learning (RL)-based adaptive resource allocation framework to address these issues. The framework models resource allocation as a Markov Decision Process (MDP) with dynamic states that include latency, resource utilization, and energy consumption. A reward function is designed to optimize the throughput, latency, and energy efficiency while ensuring fairness among tenants. The proposed model demonstrates significant improvements over heuristic approaches, achieving a 50% reduction in latency (from 250 ms to 120 ms), a 38.9% increase in throughput (from 180 tasks/s to 250 tasks/s), and a 35% improvement in energy efficiency. Additionally, the model reduces operational costs by 40%, achieves SLA compliance rates above 98%, and enhances fairness by lowering the Gini coefficient from 0.25 to 0.10. Under burst loads, the system maintains a service level objective success rate of 94% with a time to scale of 6 s. These results underscore the potential of RL-based solutions for dynamic workload management, paving the way for more scalable, cost-effective, and sustainable serverless multitenancy systems. Full article
(This article belongs to the Special Issue New Advances in Cloud Computing and Its Latest Applications)
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20 pages, 2538 KiB  
Article
Research on Long-Term Scheduling Optimization of Water–Wind–Solar Multi-Energy Complementary System Based on DDPG
by Zixing Wan, Wenwu Li, Mu He, Taotao Zhang, Shengzhe Chen, Weiwei Guan, Xiaojun Hua and Shang Zheng
Energies 2025, 18(15), 3983; https://doi.org/10.3390/en18153983 - 25 Jul 2025
Viewed by 226
Abstract
To address the challenges of high complexity in modeling the correlation of multi-dimensional stochastic variables and the difficulty of solving long-term scheduling models in continuous action spaces in multi-energy complementary systems, this paper proposes a long-term optimization scheduling method based on Deep Deterministic [...] Read more.
To address the challenges of high complexity in modeling the correlation of multi-dimensional stochastic variables and the difficulty of solving long-term scheduling models in continuous action spaces in multi-energy complementary systems, this paper proposes a long-term optimization scheduling method based on Deep Deterministic Policy Gradient (DDPG). First, an improved C-Vine Copula model is used to construct the multi-dimensional joint probability distribution of water, wind, and solar energy, and Latin Hypercube Sampling (LHS) is employed to generate a large number of water–wind–solar coupling scenarios, effectively reducing the model’s complexity. Then, a long-term optimization scheduling model is established with the goal of maximizing the absorption of clean energy, and it is converted into a Markov Decision Process (MDP). Next, the DDPG algorithm is employed with a noise dynamic adjustment mechanism to optimize the policy in continuous action spaces, yielding the optimal long-term scheduling strategy for the water–wind–solar multi-energy complementary system. Finally, using a water–wind–solar integrated energy base as a case study, comparative analysis demonstrates that the proposed method can improve the renewable energy absorption capacity and the system’s power generation efficiency by accurately quantifying the uncertainties of water, wind, and solar energy and precisely controlling the continuous action space during the scheduling process. Full article
(This article belongs to the Section B: Energy and Environment)
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26 pages, 453 KiB  
Article
Trend-Enabled Recommender System with Diversity Enhancer for Crop Recommendation
by Iulia Baraian, Rudolf Erdei, Rares Tamaian, Daniela Delinschi, Emil Marian Pasca and Oliviu Matei
Agriculture 2025, 15(15), 1614; https://doi.org/10.3390/agriculture15151614 - 25 Jul 2025
Viewed by 149
Abstract
Achieving optimal agricultural yields and promoting sustainable farming relies on accurate crop recommendations. However, the applicability of many current systems is limited by their considerable computational requirements and dependence on comprehensive datasets, especially in resource-limited contexts. This paper presents HOLISTIQ RS, a novel [...] Read more.
Achieving optimal agricultural yields and promoting sustainable farming relies on accurate crop recommendations. However, the applicability of many current systems is limited by their considerable computational requirements and dependence on comprehensive datasets, especially in resource-limited contexts. This paper presents HOLISTIQ RS, a novel crop recommendation system explicitly designed for operation on low-specification hardware and in data-scarce regions. HOLISTIQ RS combines collaborative filtering with a Markov model to predict appropriate crop choices, drawing upon user profiles, regional agricultural data, and past crop performance. Results indicate that HOLISTIQ RS provides a significant increase in recommendation accuracy, achieving a MAP@5 of 0.31 and nDCG@5 of 0.41, outperforming standard collaborative filtering methods (the KNN achieved MAP@5 of 0.28 and nDCG@5 of 0.38, and the ANN achieved MAP@5 of 0.25 and nDCG@5 of 0.35). Significantly, the system also demonstrates enhanced recommendation diversity, achieving an Item Variety (IV@5) of 23%, which is absent in deterministic baselines. Significantly, the system is engineered for reduced energy consumption and can be deployed on low-cost hardware. This provides a feasible and adaptable method for encouraging informed decision-making and promoting sustainable agricultural practices in areas where resources are constrained, with an emphasis on lower energy usage. Full article
(This article belongs to the Section Agricultural Systems and Management)
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27 pages, 8383 KiB  
Article
A Resilience Quantitative Assessment Framework for Cyber–Physical Systems: Mathematical Modeling and Simulation
by Zhigang Cao, Hantao Zhao, Yunfan Wang, Chuan He, Ding Zhou and Xiaopeng Han
Appl. Sci. 2025, 15(15), 8285; https://doi.org/10.3390/app15158285 - 25 Jul 2025
Viewed by 101
Abstract
As cyber threats continue to grow in complexity and persistence, resilience has become a critical requirement for cyber–physical systems (CPSs). Resilience quantitative assessment is essential for supporting secure system design and ensuring reliable operation. Although various methods have been proposed for evaluating CPS [...] Read more.
As cyber threats continue to grow in complexity and persistence, resilience has become a critical requirement for cyber–physical systems (CPSs). Resilience quantitative assessment is essential for supporting secure system design and ensuring reliable operation. Although various methods have been proposed for evaluating CPS resilience, major challenges remain in accurately modeling the interaction between cyber and physical domains and in providing structured guidance for resilience-oriented design. This study proposes an integrated CPS resilience assessment framework that combines cyber-layer anomaly modeling based on Markov chains with mathematical modeling of performance degradation and recovery in the physical domain. The framework establishes a structured evaluation process through parameter normalization and cyber–physical coupling, enabling the generation of resilience curves that clearly represent system performance changes under adverse conditions. A case study involving an industrial controller equipped with a diversity-redundancy architecture is conducted to demonstrate the applicability of the proposed method. Modeling and simulation results indicate that the framework effectively reveals key resilience characteristics and supports performance-informed design optimization. Full article
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33 pages, 4841 KiB  
Article
Research on Task Allocation in Four-Way Shuttle Storage and Retrieval Systems Based on Deep Reinforcement Learning
by Zhongwei Zhang, Jingrui Wang, Jie Jin, Zhaoyun Wu, Lihui Wu, Tao Peng and Peng Li
Sustainability 2025, 17(15), 6772; https://doi.org/10.3390/su17156772 - 25 Jul 2025
Viewed by 293
Abstract
The four-way shuttle storage and retrieval system (FWSS/RS) is an advanced automated warehousing solution for achieving green and intelligent logistics, and task allocation is crucial to its logistics efficiency. However, current research on task allocation in three-dimensional storage environments is mostly conducted in [...] Read more.
The four-way shuttle storage and retrieval system (FWSS/RS) is an advanced automated warehousing solution for achieving green and intelligent logistics, and task allocation is crucial to its logistics efficiency. However, current research on task allocation in three-dimensional storage environments is mostly conducted in the single-operation mode that handles inbound or outbound tasks individually, with limited attention paid to the more prevalent composite operation mode where inbound and outbound tasks coexist. To bridge this gap, this study investigates the task allocation problem in an FWSS/RS under the composite operation mode, and deep reinforcement learning (DRL) is introduced to solve it. Initially, the FWSS/RS operational workflows and equipment motion characteristics are analyzed, and a task allocation model with the total task completion time as the optimization objective is established. Furthermore, the task allocation problem is transformed into a partially observable Markov decision process corresponding to reinforcement learning. Each shuttle is regarded as an independent agent that receives localized observations, including shuttle position information and task completion status, as inputs, and a deep neural network is employed to fit value functions to output action selections. Correspondingly, all agents are trained within an independent deep Q-network (IDQN) framework that facilitates collaborative learning through experience sharing while maintaining decentralized decision-making based on individual observations. Moreover, to validate the efficiency and effectiveness of the proposed model and method, experiments were conducted across various problem scales and transport resource configurations. The experimental results demonstrate that the DRL-based approach outperforms conventional task allocation methods, including the auction algorithm and the genetic algorithm. Specifically, the proposed IDQN-based method reduces the task completion time by up to 12.88% compared to the auction algorithm, and up to 8.64% compared to the genetic algorithm across multiple scenarios. Moreover, task-related factors are found to have a more significant impact on the optimization objectives of task allocation than transport resource-related factors. Full article
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37 pages, 2373 KiB  
Article
A Quantile Spillover-Driven Markov Switching Model for Volatility Forecasting: Evidence from the Cryptocurrency Market
by Fangfang Zhu, Sicheng Fu and Xiangdong Liu
Mathematics 2025, 13(15), 2382; https://doi.org/10.3390/math13152382 - 24 Jul 2025
Viewed by 199
Abstract
This paper develops a novel modeling framework that integrates time-varying quantile-based spillover effects into a regime-switching realized volatility model. A dynamic spillover factor is constructed by identifying the most influential contributors to Bitcoin’s realized volatility across different quantile levels. This quantile-layered structure enables [...] Read more.
This paper develops a novel modeling framework that integrates time-varying quantile-based spillover effects into a regime-switching realized volatility model. A dynamic spillover factor is constructed by identifying the most influential contributors to Bitcoin’s realized volatility across different quantile levels. This quantile-layered structure enables the model to capture heterogeneous spillover paths under varying market conditions at a macro level while also enhancing the sensitivity of volatility regime identification via its incorporation into a time-varying transition probability (TVTP) Markov-switching mechanism at a micro level. Empirical results based on the cryptocurrency market demonstrate the superior forecasting performance of the proposed TVTP-MS-HAR model relative to standard benchmark models. The model exhibits strong capability in identifying state-dependent spillovers and capturing nonlinear market dynamics. The findings further reveal an asymmetric dual-tail amplification and time-varying interconnectedness in the spillover effects, along with a pronounced asymmetry between market capitalization and systemic importance. Compared to decomposition-based approaches, the X-RV type of models—especially when combined with the proposed quantile-driven factor—offers improved robustness and predictive accuracy in the presence of extreme market behavior. This paper offers a coherent approach that bridges phenomenon identification, source localization, and predictive mechanism construction, contributing to both the academic understanding and practical risk assessment of cryptocurrency markets. Full article
(This article belongs to the Section E5: Financial Mathematics)
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17 pages, 2885 KiB  
Article
Energy Management of Electric–Hydrogen Coupled Integrated Energy System Based on Improved Proximal Policy Optimization Algorithm
by Jingbo Zhao, Zhengping Gao and Zhe Chen
Energies 2025, 18(15), 3925; https://doi.org/10.3390/en18153925 - 23 Jul 2025
Viewed by 298
Abstract
The electric–hydrogen coupled integrated energy system (EHCS) is a critical pathway for the low-carbon transition of energy systems. However, the inherent uncertainties of renewable energy sources present significant challenges to optimal energy management in the EHCS. To address these challenges, this paper proposes [...] Read more.
The electric–hydrogen coupled integrated energy system (EHCS) is a critical pathway for the low-carbon transition of energy systems. However, the inherent uncertainties of renewable energy sources present significant challenges to optimal energy management in the EHCS. To address these challenges, this paper proposes an energy management method for the EHCS based on an improved proximal policy optimization (IPPO) algorithm. This method aims to overcome the limitations of traditional heuristic algorithms, such as low solution accuracy, and the inefficiencies of mathematical programming methods. First, a mathematical model for the EHCS is established. Then, by introducing the Markov decision process (MDP), this mathematical model is transformed into a deep reinforcement learning framework. On this basis, the state space and action space of the system are defined, and a reward function is designed to guide the agent to learn to the optimal strategy, which takes into account the constraints of the system. Finally, the efficacy and economic viability of the proposed method are validated through numerical simulation. Full article
(This article belongs to the Special Issue Advances in Hydrogen Energy and Power System)
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18 pages, 1138 KiB  
Article
Intelligent Priority-Aware Spectrum Access in 5G Vehicular IoT: A Reinforcement Learning Approach
by Adeel Iqbal, Tahir Khurshaid and Yazdan Ahmad Qadri
Sensors 2025, 25(15), 4554; https://doi.org/10.3390/s25154554 - 23 Jul 2025
Viewed by 251
Abstract
Efficient and intelligent spectrum access is crucial for meeting the diverse Quality of Service (QoS) demands of Vehicular Internet of Things (V-IoT) systems in next-generation cellular networks. This work proposes a novel reinforcement learning (RL)-based priority-aware spectrum management (RL-PASM) framework, a centralized self-learning [...] Read more.
Efficient and intelligent spectrum access is crucial for meeting the diverse Quality of Service (QoS) demands of Vehicular Internet of Things (V-IoT) systems in next-generation cellular networks. This work proposes a novel reinforcement learning (RL)-based priority-aware spectrum management (RL-PASM) framework, a centralized self-learning priority-aware spectrum management framework operating through Roadside Units (RSUs). RL-PASM dynamically allocates spectrum resources across three traffic classes: high-priority (HP), low-priority (LP), and best-effort (BE), utilizing reinforcement learning (RL). This work compares four RL algorithms: Q-Learning, Double Q-Learning, Deep Q-Network (DQN), and Actor-Critic (AC) methods. The environment is modeled as a discrete-time Markov Decision Process (MDP), and a context-sensitive reward function guides fairness-preserving decisions for access, preemption, coexistence, and hand-off. Extensive simulations conducted under realistic vehicular load conditions evaluate the performance across key metrics, including throughput, delay, energy efficiency, fairness, blocking, and interruption probability. Unlike prior approaches, RL-PASM introduces a unified multi-objective reward formulation and centralized RSU-based control to support adaptive priority-aware access for dynamic vehicular environments. Simulation results confirm that RL-PASM balances throughput, latency, fairness, and energy efficiency, demonstrating its suitability for scalable and resource-constrained deployments. The results also demonstrate that DQN achieves the highest average throughput, followed by vanilla QL. DQL and AC maintain fairness at high levels and low average interruption probability. QL demonstrates the lowest average delay and the highest energy efficiency, making it a suitable candidate for edge-constrained vehicular deployments. Selecting the appropriate RL method, RL-PASM offers a robust and adaptable solution for scalable, intelligent, and priority-aware spectrum access in vehicular communication infrastructures. Full article
(This article belongs to the Special Issue Emerging Trends in Next-Generation mmWave Cognitive Radio Networks)
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30 pages, 1981 KiB  
Article
Stochastic Control for Sustainable Hydrogen Generation in Standalone PV–Battery–PEM Electrolyzer Systems
by Mohamed Aatabe, Wissam Jenkal, Mohamed I. Mosaad and Shimaa A. Hussien
Energies 2025, 18(15), 3899; https://doi.org/10.3390/en18153899 - 22 Jul 2025
Viewed by 343
Abstract
Standalone photovoltaic (PV) systems offer a viable path to decentralized energy access but face limitations during periods of low solar irradiance. While batteries provide short-term storage, their capacity constraints often restrict the use of surplus energy, highlighting the need for long-duration solutions. Green [...] Read more.
Standalone photovoltaic (PV) systems offer a viable path to decentralized energy access but face limitations during periods of low solar irradiance. While batteries provide short-term storage, their capacity constraints often restrict the use of surplus energy, highlighting the need for long-duration solutions. Green hydrogen, generated via proton exchange membrane (PEM) electrolyzers, offers a scalable alternative. This study proposes a stochastic energy management framework that leverages a Markov decision process (MDP) to coordinate PV generation, battery storage, and hydrogen production under variable irradiance and uncertain load demand. The strategy dynamically allocates power flows, ensuring system stability and efficient energy utilization. Real-time weather data from Goiás, Brazil, is used to simulate system behavior under realistic conditions. Compared to the conventional perturb and observe (P&O) technique, the proposed method significantly improves system performance, achieving a 99.9% average efficiency (vs. 98.64%) and a drastically lower average tracking error of 0.3125 (vs. 9.8836). This enhanced tracking accuracy ensures faster convergence to the maximum power point, even during abrupt load changes, thereby increasing the effective use of solar energy. As a direct consequence, green hydrogen production is maximized while energy curtailment is minimized. The results confirm the robustness of the MDP-based control, demonstrating improved responsiveness, reduced downtime, and enhanced hydrogen yield, thus supporting sustainable energy conversion in off-grid environments. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
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22 pages, 3091 KiB  
Article
Assessment of the Risk of Failure in Electric Power Supply Systems for Railway Traffic Control Devices
by Tomasz Ciszewski, Jerzy Wojciechowski, Mieczysław Kornaszewski, Grzegorz Krawczyk, Beata Kuźmińska-Sołśnia and Artur Hermanowicz
Sensors 2025, 25(14), 4501; https://doi.org/10.3390/s25144501 - 19 Jul 2025
Viewed by 349
Abstract
This paper provides a reliability analysis of selected components in the electrical power supply systems used for railway traffic control equipment. It includes rectifiers, controllers, inverters, generators, batteries, sensors, and switching elements. The study used failure data from power supply system elements on [...] Read more.
This paper provides a reliability analysis of selected components in the electrical power supply systems used for railway traffic control equipment. It includes rectifiers, controllers, inverters, generators, batteries, sensors, and switching elements. The study used failure data from power supply system elements on selected railway lines. The analysis was performed using a mathematical model based on Markov processes. Based on the findings, recommendations were made to improve safety levels. The results presented in the paper could serve as a valuable source of information for operators of power supply systems in railway traffic control, helping them optimize maintenance processes and increase equipment reliability. Full article
(This article belongs to the Special Issue Diagnosis and Risk Analysis of Electrical Systems)
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14 pages, 370 KiB  
Article
Stabilization of Stochastic Dynamic Systems with Markov Parameters and Concentration Point
by Taras Lukashiv, Igor V. Malyk, Venkata P. Satagopam and Petr V. Nazarov
Mathematics 2025, 13(14), 2307; https://doi.org/10.3390/math13142307 - 19 Jul 2025
Viewed by 234
Abstract
This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, [...] Read more.
This paper addresses the problem of optimal stabilization for stochastic dynamical systems characterized by Markov switches and concentration points of jumps, which is a scenario not adequately covered by classical stability conditions. Unlike traditional approaches requiring a strictly positive minimal interval between jumps, we allow jump moments to accumulate at a finite point. Utilizing Lyapunov function methods, we derive sufficient conditions for exponential stability in the mean square and asymptotic stability in probability. We provide explicit constructions of Lyapunov functions adapted to scenarios with jump concentration points and develop conditions under which these functions ensure system stability. For linear stochastic differential equations, the stabilization problem is further simplified to solving a system of Riccati-type matrix equations. This work provides essential theoretical foundations and practical methodologies for stabilizing complex stochastic systems that feature concentration points, expanding the applicability of optimal control theory. Full article
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