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29 pages, 2795 KB  
Article
A Methodological Framework for Assessing Cultural Identity Potential in Sustainable Cultural Tourism: The Case of Cross River State, Nigeria
by Leki Clementina Pronen and Mukaddes Polay
Sustainability 2026, 18(6), 2744; https://doi.org/10.3390/su18062744 - 11 Mar 2026
Cited by 1 | Viewed by 317
Abstract
Tourism destinations are constantly invoking culture into the sustainability agenda, yet existing tourism sustainability indicator frameworks overemphasize environmental and economic metrics, and cultural identity is often marginalized or addressed through fragmented heritage measures, thereby restricting tourism destinations from effectively evaluating their potential to [...] Read more.
Tourism destinations are constantly invoking culture into the sustainability agenda, yet existing tourism sustainability indicator frameworks overemphasize environmental and economic metrics, and cultural identity is often marginalized or addressed through fragmented heritage measures, thereby restricting tourism destinations from effectively evaluating their potential to sustain and reinforce identity within the context of sustainable cultural tourism. In this view, cultural identity potential (CIP), defined as a destination’s capacity to sustain and transmit cultural identity in cultural tourism, remains under-operationalized in existing destination assessments. To address this gap, this study develops a comprehensive indicator-based framework to assess the cultural identity potential in sustainable cultural tourism. A two-phase design method was adopted: (1) a multi-step process to scope sustainable cultural tourism dimensions and operationalize CIP into criteria and indicators; and (2) a modified Delphi technique to refine and validate key criteria and indicators. A regional panel of 25 academic and non-academic experts participated in round 1, while 18 participated in round 2. The finalized framework comprises 39 criteria and 110 indicators (79% of the initial 139 items) across the destination management, economic, social, cultural, and environmental dimensions. Consensus increased across rounds, demonstrating convergence, with stability testing demonstrating that 91.2% of the re-rated indicators did not change significantly (p ≥ 0.05), supporting consistency of retained items. Overall, the CIP framework provides a policy-ready tool for evaluating and monitoring cultural identity potential in Cross River State and similar regions, serving as a reference for practitioners in sustainable cultural tourism development. Full article
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26 pages, 706 KB  
Article
Efficient Federated Learning Method FedLayerPrune Based on Layer Adaptive Pruning
by Wenlong He, Hui Cao, Jisai Zhang and Decao Yang
Electronics 2026, 15(5), 1049; https://doi.org/10.3390/electronics15051049 - 2 Mar 2026
Viewed by 356
Abstract
As a privacy-preserving distributed machine learning paradigm, federated learning (FL) faces serious communication bottlenecks in practical deployment. In this paper, we propose FedLayerPrune, a communication-efficient federated learning method that integrates three synergistic components: (i) a layer-adaptive pruning strategy that dynamically allocates pruning rates [...] Read more.
As a privacy-preserving distributed machine learning paradigm, federated learning (FL) faces serious communication bottlenecks in practical deployment. In this paper, we propose FedLayerPrune, a communication-efficient federated learning method that integrates three synergistic components: (i) a layer-adaptive pruning strategy that dynamically allocates pruning rates based on layer sensitivity and network depth; (ii) a heterogeneity-aware aggregation mechanism that combines sample-size weighted averaging with mask consensus voting to enhance robustness under non-IID data distributions; and (iii) a dynamic pruning rate scheduler that progressively increases compression intensity across training rounds. Unlike existing approaches that apply uniform pruning or consider these techniques in isolation, FedLayerPrune achieves a principled coordination among layer-wise importance evaluation, temporal pruning scheduling, and heterogeneous model aggregation. Extensive experiments on CIFAR-10, MNIST, and Fashion-MNIST demonstrate that FedLayerPrune reduces communication costs by up to 68.3% compared with standard FedAvg, while maintaining model accuracy within a 2% margin. Moreover, our method exhibits stronger robustness and faster convergence under severe non-IID data distributions. These results suggest that FedLayerPrune provides a practical and effective solution for deploying federated learning in resource-constrained edge computing environments. Full article
(This article belongs to the Section Computer Science & Engineering)
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28 pages, 1786 KB  
Article
Measuring Assistive Technology Outcomes via AI-Based Kinematic Modeling of Individualized Routine Learning in Elite Boccia Athletes with Severe Cerebral Palsy: A Longitudinal Case Series
by Se-Won Park and Young-Kyun Ha
Bioengineering 2026, 13(3), 261; https://doi.org/10.3390/bioengineering13030261 - 25 Feb 2026
Viewed by 415
Abstract
Objectives: This longitudinal single-case series evaluated an AI-based routine-learning system as assistive technology (AT) for elite Boccia athletes with severe Cerebral Palsy (CP). The study aimed to provide an innovative outcome measurement approach for individualized monitoring by integrating performance scores and longitudinal kinematic [...] Read more.
Objectives: This longitudinal single-case series evaluated an AI-based routine-learning system as assistive technology (AT) for elite Boccia athletes with severe Cerebral Palsy (CP). The study aimed to provide an innovative outcome measurement approach for individualized monitoring by integrating performance scores and longitudinal kinematic variability indicators. Methods: Three national-level players performed 694 throws over eight weeks. To ensure technical credibility, trials were rated through a consensus-based assessment by a panel of two experts, serving as ground truth for AI modeling. The system utilized a Bidirectional Long Short-Term Memory (Bi-LSTM) architecture to extract 29 kinematic features and perform regression-based scoring, providing real-time augmented feedback. Results: High-baseline tasks maintained stable scores (7–9), while intermediate tasks showed significant score increases, reflecting motor learning transitions. The model achieved a Mean Squared Error of 1.14 and a Mean Absolute Error of 1.13, demonstrating high alignment with expert standards. Training demonstrated stable convergence, with loss reducing from 7.45 to 1.19. Notably, for the most severely impaired athlete, the AI system detected a 4.69% reduction in kinematic variability despite stagnant performance scores. This provides empirical evidence of movement stabilization within the cognitive stage that traditional observation might overlook. Conclusions: The Bi-LSTM system enabled accurate tracking of performance and motor variability, revealing distinct learning curves based on task difficulty. These findings demonstrate the feasibility of AI-enabled motion analysis as an AT for outcome measurement, supporting data-driven coaching where conventional evaluation is constrained by the rarity and severity of disabilities. Full article
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17 pages, 4851 KB  
Article
Distributed Particle Swarm Optimization with Dimension-Level Interactions for Large-Scale Separable Optimization Problems
by Tingting Xiao, Qiang Li and Jun Zhang
Processes 2026, 14(4), 642; https://doi.org/10.3390/pr14040642 - 12 Feb 2026
Viewed by 333
Abstract
Optimization problems for large-scale distributed systems are challenging due to their complexities. In an attempt to solve these problems, centralized intelligence algorithms suffer from large computational costs and slow convergence rates. Therefore, in this paper, a distributed particle swarm optimization (MDPSO) algorithm is [...] Read more.
Optimization problems for large-scale distributed systems are challenging due to their complexities. In an attempt to solve these problems, centralized intelligence algorithms suffer from large computational costs and slow convergence rates. Therefore, in this paper, a distributed particle swarm optimization (MDPSO) algorithm is proposed. To reduce computational costs, a dimension-level interaction is introduced, and an average consensus operator is incorporated for accelerating convergence rates. In the distributed method, each agent is assigned only a single particle, rather than a subpopulation in traditional PSO. Furthermore, every particle position is decomposed into two sub-vectors that are processed separately, significantly improving convergence rate and solution accuracy. Moreover, a theorem and a corollary are presented, which guarantee the consensus convergence of the proposed method. Finally, three cases are designed. The results show that our method requires only half the number of iterations compared to other methods. Additionally, it finds optima with higher accuracy. More importantly, compared to the variants of PSO, only 1/N of the total particle population is used, which reduces the computational costs significantly. Full article
(This article belongs to the Special Issue Modeling and Simulation of Robot Intelligent Control System)
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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 359
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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43 pages, 9485 KB  
Article
Dynamic Task Allocation for Multiple AUVs Under Weak Underwater Acoustic Communication: A CBBA-Based Simulation Study
by Hailin Wang, Shuo Li, Tianyou Qiu, Yiqun Wang and Yiping Li
J. Mar. Sci. Eng. 2026, 14(3), 237; https://doi.org/10.3390/jmse14030237 - 23 Jan 2026
Viewed by 515
Abstract
Cooperative task allocation is one of the critical enablers for multi-Autonomous Underwater Vehicle (AUV) missions, but existing approaches often assume reliable communication that rarely holds in real underwater acoustic environments. We study here the performance and robustness of the Consensus-Based Bundle Algorithm (CBBA) [...] Read more.
Cooperative task allocation is one of the critical enablers for multi-Autonomous Underwater Vehicle (AUV) missions, but existing approaches often assume reliable communication that rarely holds in real underwater acoustic environments. We study here the performance and robustness of the Consensus-Based Bundle Algorithm (CBBA) for multi-AUV task allocation under realistically degraded underwater communication conditions with dynamically appearing tasks. An integrated simulation framework that incorporates a Dubins-based kinematic model with minimum turning radius constraints, a configurable underwater acoustic communication model (range, delay, packet loss, and bandwidth), and a full implementation of improved CBBA with new features, complemented by 3D trajectory and network-topology visualization. We define five communication regimes, from ideal fully connected networks to severe conditions with short range and high packet loss. Within these regimes, we assess CBBA based on task allocation quality (total bundle value and task completion rate), convergence behavior (iterations and convergence rate), and communication efficiency (message delivery rate, average delay, and network connectivity), with additional metrics on the number of conflicts during dynamic task reallocation. Our simulation results indicate that CBBA maintains performance close to the optimum when the conditions are good and moderate but degrades significantly when connectivity becomes intermittent. We then introduce a local-communication-based conflict resolution strategy in the face of frequent task conflicts under very poor conditions: neighborhood-limited information exchange, negotiation within task areas, and decentralized local decisions. The proposed conflict resolution strategy significantly reduces the occurrence of conflicts and improves task completion under stringent communication constraints. This provides practical design insights for deploying multi-AUV systems under weak underwater acoustic networks. Full article
(This article belongs to the Special Issue Dynamics and Control of Marine Mechatronics)
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14 pages, 808 KB  
Article
UnderstandingDelirium.ca: A Mixed-Methods Observational Evaluation of an Internet-Based Educational Intervention for the Public and Care Partners
by Randi Shen, Dima Hadid, Stephanie Ayers, Sandra Clark, Rebekah Woodburn, Roland Grad and Anthony J. Levinson
Geriatrics 2025, 10(6), 168; https://doi.org/10.3390/geriatrics10060168 - 16 Dec 2025
Viewed by 556
Abstract
Background/Objectives: Delirium, an acute cognitive disturbance, is often unrecognized by family or friend care partners, contributing to delayed interventions and negative health outcomes. UnderstandingDelirium.ca is an e-learning lesson developed to address this gap by improving delirium knowledge among the public, patients, and family/friend [...] Read more.
Background/Objectives: Delirium, an acute cognitive disturbance, is often unrecognized by family or friend care partners, contributing to delayed interventions and negative health outcomes. UnderstandingDelirium.ca is an e-learning lesson developed to address this gap by improving delirium knowledge among the public, patients, and family/friend care partners. Our objective was to evaluate the acceptability, intention to use, and perceived impact of Understanding Delirium e-learning among public users. Methods: A convergent mixed-methods observational evaluation combining survey-based quantitative data and thematic analysis was conducted. The survey included the Net Promoter Score (NPS), the short-form Information Assessment Method for patients and consumers (IAM4all-SF), and an open-text feedback item. Descriptive statistics were used to summarize IAM4all-SF responses, assessing perceived relevance, understandability, intended use, and anticipated benefit. Open-text comments were analyzed thematically by two independent reviewers who reached consensus through discussion. Subgroup analysis of qualitative themes was performed by age, gender, and NPS category. Results: Among 629 survey respondents, over 90% of respondents agreed that the lesson was relevant, understandable, likely to be used, and beneficial. The NPS was rated ‘excellent’ (score of 71), and lesson uptake included over 7000 unique users with a 35% completion rate. Qualitative analysis revealed themes of high educational value, emotional resonance, and perceived gaps in prior healthcare communication. Respondents emphasized the lesson’s clarity, intent to share, and potential for wider dissemination. Conclusions: UnderstandingDelirium.ca is a promising, guideline-aligned digital intervention that has potential to enhance delirium literacy and reduce care partner distress. Findings suggest that the Understanding Delirium e-learning can effectively improve public delirium literacy and should be integrated into care partner and clinical workflows. Full article
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34 pages, 8174 KB  
Article
Formation Control of Underactuated AUVs Based on Event-Triggered Communication and Fractional-Order Sliding Mode Control
by Long He, Ya Zhang, Shizhong Li, Bo Li, Mengting Xie, Zehui Yuan and Chenrui Bai
Fractal Fract. 2025, 9(12), 755; https://doi.org/10.3390/fractalfract9120755 - 21 Nov 2025
Cited by 3 | Viewed by 838
Abstract
To address the challenges faced by multiple autonomous underwater vehicles (AUVs) in formation control under complex marine environments—such as model uncertainties, external disturbances, dynamic communication topology variations, and limited communication resources—this paper proposes an integrated control framework that combines robust individual control, distributed [...] Read more.
To address the challenges faced by multiple autonomous underwater vehicles (AUVs) in formation control under complex marine environments—such as model uncertainties, external disturbances, dynamic communication topology variations, and limited communication resources—this paper proposes an integrated control framework that combines robust individual control, distributed cooperative formation, and dynamic event-triggered communication. At the individual control level, a robust control method based on a fractional-order sliding mode observer (FOSMO) and a fractional-order terminal sliding mode controller (FOTSMC) is developed. The observer exploits the memory and broadband characteristics of fractional calculus to achieve high-precision estimation of lumped disturbances, while the controller constructs a non-integer-order sliding surface with an adaptive gain law to guarantee finite-time convergence of tracking errors. At the formation coordination level, a distributed trajectory generation method based on dynamic consensus is proposed to achieve reference trajectory planning and formation maintenance in a cooperative manner. At the communication level, a dynamic-threshold event-triggered mechanism is designed, where the triggering condition is adaptively adjusted according to the state errors, thereby significantly reducing communication load and energy consumption. Theoretically, Lyapunov-based analysis rigorously proves the stability and convergence of the closed-loop system. Numerical simulations confirm that the proposed method outperforms several benchmark algorithms in terms of tracking accuracy and disturbance rejection. Moreover, the integrated framework maintains precise formation under communication topology variations, achieving a communication reduction rate exceeding 65% compared to periodic protocols while preserving coordination accuracy. Full article
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8 pages, 532 KB  
Proceeding Paper
Developing Bio-Inspired Sustainability Assessment Tool: The Role of Energy Efficiency
by Olusegun Oguntona
Eng. Proc. 2025, 114(1), 9; https://doi.org/10.3390/engproc2025114009 - 5 Nov 2025
Viewed by 502
Abstract
The escalating demand for sustainable development in the built environment necessitates the integration of innovative, system-based assessment tools. This study investigates the role of energy efficiency (EE) within a nature-inspired sustainability assessment framework, drawing from biomimicry principles to evaluate green building practices in [...] Read more.
The escalating demand for sustainable development in the built environment necessitates the integration of innovative, system-based assessment tools. This study investigates the role of energy efficiency (EE) within a nature-inspired sustainability assessment framework, drawing from biomimicry principles to evaluate green building practices in South Africa. Grounded in the ethos of nature’s efficiency, such as closed-loop energy systems, passive energy use, efficiency through form and function, and decentralised and localised energy generation, this study identifies and prioritises key EE criteria, including efficient energy management, renewable energy optimisation, passive heating, ventilation and air conditioning (HVAC) systems, and energy-saving technologies. Using the Analytic Hierarchy Process (AHP), this research engaged 38 highly experienced, practising, and registered construction professionals to perform pairwise comparisons of EE criteria. Results revealed that efficient energy management (29.8%) emerged as the most significant factor, followed closely by energy-saving equipment (26.4%), with strong expert consensus (consistency ratio = 0.03). The findings reflect a convergence of ecological wisdom and industry expertise, suggesting that nature’s design strategies offer a compelling roadmap for achieving sustainable energy performance in buildings. This study reinforces the applicability of biomimicry in shaping context-specific sustainability metrics and informs the development of adaptive, ecologically aligned certification frameworks. This study recommends the integration of these EE criteria into building rating systems, fostering interdisciplinary collaboration, and scaling nature-based frameworks to inform global sustainability practice. By bridging theory and application, this study advances a regenerative approach to construction that aligns with the UN Sustainable Development Goals and long-term environmental resilience. Full article
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18 pages, 1872 KB  
Article
Consensus-Driven Evaluation of Current Practices and Innovation Feasibility in Chronic Brain Injury Rehabilitation
by Helena Bascuñana-Ambrós, Lourdes Gil-Fraguas, Carolina De Miguel-Benadiba, Jan Ferrer-Picó, Michelle Catta-Preta, Alex Trejo-Omeñaca and Josep Maria Monguet-Fierro
Healthcare 2025, 13(21), 2725; https://doi.org/10.3390/healthcare13212725 - 28 Oct 2025
Viewed by 891
Abstract
Background: Chronic Brain Injury (CBI) is a lifelong condition requiring continuous adaptation by patients, families, and healthcare professionals. Transitioning rehabilitation toward patient-centered and self-management approaches is essential, yet remains limited in Spain. Methods: We conducted a two-phase consensus study in collaboration with the [...] Read more.
Background: Chronic Brain Injury (CBI) is a lifelong condition requiring continuous adaptation by patients, families, and healthcare professionals. Transitioning rehabilitation toward patient-centered and self-management approaches is essential, yet remains limited in Spain. Methods: We conducted a two-phase consensus study in collaboration with the Spanish Society of Physical Medicine and Rehabilitation (SERMEF) and the Spanish Federation of Brain Injury (FEDACE). In Phase 1, surveys were distributed to patients (214 invited; 95 complete responses, 44.4%) and physiatrists (256 invited; 106 valid responses, 41.4%) to capture perceptions of current rehabilitation practices, including tele-rehabilitation. Differences and convergences between groups were analyzed using a Synthetic Factor (F). In Phase 2, a panel of 21 experts applied a real-time eDelphi process (SmartDelphi) to assess the feasibility of proposed innovations, rated on a six-point Likert scale. Results: Patients and professionals showed both alignment and divergence in their views. Patients reported lower involvement of rehabilitation teams and expressed more reluctance toward replacing in-person care with telemedicine. However, both groups endorsed hybrid models and emphasized the importance of improved communication tools. Expert consensus prioritized feasible interventions such as online orthopedic renewal services, hybrid care models, and educational video resources, while less feasible options included informal communication platforms (e.g., WhatsApp) and bidirectional teleconsultations. Recommendations were consolidated into five domains: (R1) systemic involvement of rehabilitation teams in chronic care, (R2) patient and caregiver education, (R3) self-management support, (R4) communication tools, and (R5) socialization strategies. Conclusions: This study demonstrates the value of combining patient and professional perspectives through digital Delphi methods to co-design innovation strategies in CBI rehabilitation. Findings highlight the need to strengthen communication, provide structured education, and implement hybrid care models to advance patient-centered rehabilitation. The methodology itself fostered engagement and consensus, underscoring its potential as a tool for participatory healthcare planning. Full article
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18 pages, 2863 KB  
Article
Using Non-Lipschitz Signum-Based Functions for Distributed Optimization and Machine Learning: Trade-Off Between Convergence Rate and Optimality Gap
by Mohammadreza Doostmohammadian, Amir Ahmad Ghods, Alireza Aghasi, Zulfiya R. Gabidullina and Hamid R. Rabiee
Math. Comput. Appl. 2025, 30(5), 108; https://doi.org/10.3390/mca30050108 - 4 Oct 2025
Viewed by 1009
Abstract
In recent years, the prevalence of large-scale datasets and the demand for sophisticated learning models have necessitated the development of efficient distributed machine learning (ML) solutions. Convergence speed is a critical factor influencing the practicality and effectiveness of these distributed frameworks. Recently, non-Lipschitz [...] Read more.
In recent years, the prevalence of large-scale datasets and the demand for sophisticated learning models have necessitated the development of efficient distributed machine learning (ML) solutions. Convergence speed is a critical factor influencing the practicality and effectiveness of these distributed frameworks. Recently, non-Lipschitz continuous optimization algorithms have been proposed to improve the slow convergence rate of the existing linear solutions. The use of signum-based functions was previously considered in consensus and control literature to reach fast convergence in the prescribed time and also to provide robust algorithms to noisy/outlier data. However, as shown in this work, these algorithms lead to an optimality gap and steady-state residual of the objective function in discrete-time setup. This motivates us to investigate the distributed optimization and ML algorithms in terms of trade-off between convergence rate and optimality gap. In this direction, we specifically consider the distributed regression problem and check its convergence rate by applying both linear and non-Lipschitz signum-based functions. We check our distributed regression approach by extensive simulations. Our results show that although adopting signum-based functions may give faster convergence, it results in large optimality gaps. The findings presented in this paper may contribute to and advance the ongoing discourse of similar distributed algorithms, e.g., for distributed constrained optimization and distributed estimation. Full article
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16 pages, 967 KB  
Article
Research on the Consensus Convergence Rate of Multi-Agent Systems Based on Hermitian Kirchhoff Index Measurement
by He Deng and Tingzeng Wu
Entropy 2025, 27(10), 1035; https://doi.org/10.3390/e27101035 - 2 Oct 2025
Viewed by 786
Abstract
Multi-agent systems (MAS) typically model interaction topologies using directed or undirected graphs when analyzing consensus convergence rates. However, as system complexity increases, purely directed or undirected networks may be insufficient to capture interaction heterogeneity. This paper adopts hybrid networks as interaction topology to [...] Read more.
Multi-agent systems (MAS) typically model interaction topologies using directed or undirected graphs when analyzing consensus convergence rates. However, as system complexity increases, purely directed or undirected networks may be insufficient to capture interaction heterogeneity. This paper adopts hybrid networks as interaction topology to investigate strategies for improving consensus convergence rates. We propose the Hermitian Kirchhoff index, a novel metric based on resistance distance, to quantify the consensus convergence rates and establish its theoretical justification. We then examine how adding or removing edges/arcs affects the Hermitian Kirchhoff index, employing first-order eigenvalue perturbation analysis to relate these changes to algebraic connectivity and its associated eigenvectors. Numerical simulations corroborate the theoretical findings and demonstrate the effectiveness of the proposed approach. Full article
(This article belongs to the Section Complexity)
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21 pages, 4297 KB  
Article
Resilient Consensus-Based Target Tracking Under False Data Injection Attacks in Multi-Agent Networks
by Amir Ahmad Ghods and Mohammadreza Doostmohammadian
Signals 2025, 6(3), 44; https://doi.org/10.3390/signals6030044 - 2 Sep 2025
Cited by 2 | Viewed by 1670
Abstract
Distributed target tracking in multi-agent networks plays a critical role in cooperative sensing and autonomous navigation. However, it faces significant challenges in highly dynamic and adversarial setups. This study aims to enhance the resilience of decentralized target tracking algorithms against measurement faults and [...] Read more.
Distributed target tracking in multi-agent networks plays a critical role in cooperative sensing and autonomous navigation. However, it faces significant challenges in highly dynamic and adversarial setups. This study aims to enhance the resilience of decentralized target tracking algorithms against measurement faults and cyber–physical threats, especially false data injection attacks. We propose a consensus-based estimation algorithm that integrates a nearly constant velocity model with saturation-based filtering to suppress impulsive measurement variations and promote robust, distributed state estimation. To counteract adversarial conditions, we incorporate a dynamic false data injection detection and isolation mechanism that uses innovation thresholds to identify and disregard suspicious measurements before they can degrade the global estimate. The effectiveness of the proposed algorithms is demonstrated through a series of simulation-based case studies under both benign and adversarial conditions. The results show that increased network connectivity and higher consensus iteration rates improve estimation accuracy and convergence speed, while properly tuned saturation filters achieve a practical balance between fault suppression and accurate estimation. Furthermore, under localized, coordinated, and transient false data injection attacks, the detection mechanism successfully identifies compromised agents and prevents their data from corrupting the distributed global estimate. Overall, this study illustrates that the proposed algorithm provides a simplified fault-tolerant solution that significantly enhances the accuracy and resilience of distributed target tracking without imposing excessive communication or computational burdens. Full article
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25 pages, 1507 KB  
Article
DARN: Distributed Adaptive Regularized Optimization with Consensus for Non-Convex Non-Smooth Composite Problems
by Cunlin Li and Yinpu Ma
Symmetry 2025, 17(7), 1159; https://doi.org/10.3390/sym17071159 - 20 Jul 2025
Viewed by 734
Abstract
This paper proposes a Distributed Adaptive Regularization Algorithm (DARN) for solving composite non-convex and non-smooth optimization problems in multi-agent systems. The algorithm employs a three-phase iterative framework to achieve efficient collaborative optimization: (1) a local regularized optimization step, which utilizes proximal mappings to [...] Read more.
This paper proposes a Distributed Adaptive Regularization Algorithm (DARN) for solving composite non-convex and non-smooth optimization problems in multi-agent systems. The algorithm employs a three-phase iterative framework to achieve efficient collaborative optimization: (1) a local regularized optimization step, which utilizes proximal mappings to enforce strong convexity of weakly convex objectives and ensure subproblem well-posedness; (2) a consensus update based on doubly stochastic matrices, guaranteeing asymptotic convergence of agent states to a global consensus point; and (3) an innovative adaptive regularization mechanism that dynamically adjusts regularization strength using local function value variations to balance stability and convergence speed. Theoretical analysis demonstrates that the algorithm maintains strict monotonic descent under non-convex and non-smooth conditions by constructing a mixed time-scale Lyapunov function, achieving a sublinear convergence rate. Notably, we prove that the projection-based update rule for regularization parameters preserves lower-bound constraints, while spectral decay properties of consensus errors and perturbations from local updates are globally governed by the Lyapunov function. Numerical experiments validate the algorithm’s superiority in sparse principal component analysis and robust matrix completion tasks, showing a 6.6% improvement in convergence speed and a 51.7% reduction in consensus error compared to fixed-regularization methods. This work provides theoretical guarantees and an efficient framework for distributed non-convex optimization in heterogeneous networks. Full article
(This article belongs to the Section Mathematics)
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18 pages, 738 KB  
Article
PD-like Consensus Tracking Algorithm for Discrete Multi-Agent Systems with Time-Varying Reference State Under Binary-Valued Communication
by Yuqi Wu, Xu Sun, Ting Wang and Jie Wang
Actuators 2025, 14(6), 267; https://doi.org/10.3390/act14060267 - 28 May 2025
Cited by 1 | Viewed by 1154
Abstract
In this paper, a new consensus tracking control algorithm is proposed for discrete multi-agent systems under binary communication with noise and a time-varying reference state. Unlike previous studies, the leader’s reference state is time-varying and convergent. Each agent estimates its neighbors’ states using [...] Read more.
In this paper, a new consensus tracking control algorithm is proposed for discrete multi-agent systems under binary communication with noise and a time-varying reference state. Unlike previous studies, the leader’s reference state is time-varying and convergent. Each agent estimates its neighbors’ states using a recursive projection algorithm based on noisy binary-valued information. The controller design incorporates both the error between the current and estimated states and the rate of change of the estimated state, resulting in a proportional–derivative-like algorithm (PD-like algorithm). The algorithm achieves consensus tracking with a convergence rate of O(1/tε) under certain conditions. Finally, numerical simulations demonstrate the algorithm’s effectiveness and validate the theoretical results. Full article
(This article belongs to the Special Issue Advances in Intelligent Control of Actuator Systems)
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