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Search Results (1,005)

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Keywords = radial basis function neural network

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30 pages, 12446 KB  
Article
ASPSO-Optimized RBF-IITSMC for High-Precision Trajectory Tracking of 6-DOF Robotic Arms Under Uncertainties
by Duanyuan Bai, Wenbin Xie, Qiyue Yuan, Guanyu Rong and Kaichao Yang
Mathematics 2026, 14(15), 2757; https://doi.org/10.3390/math14152757 - 3 Aug 2026
Viewed by 147
Abstract
To address high-precision trajectory tracking challenges in multi-joint robots facing model uncertainties, complex friction, and abrupt disturbances, this paper proposes a radial basis function (RBF) neural network-improved integral terminal sliding mode control scheme optimized by state-aware adaptive particle swarm optimization (ASPSO), denoted as [...] Read more.
To address high-precision trajectory tracking challenges in multi-joint robots facing model uncertainties, complex friction, and abrupt disturbances, this paper proposes a radial basis function (RBF) neural network-improved integral terminal sliding mode control scheme optimized by state-aware adaptive particle swarm optimization (ASPSO), denoted as ASPSO-optimized RBF-IITSMC. First, a fractional-memory integral terminal sliding surface incorporating a boundary-layer saturation mapping is constructed. The proposed terminal mapping is shown to be globally Lipschitz continuous, and an explicit approximation-error bound relative to the conventional terminal power mapping is established. Second, an RBF neural compensator driven by the sliding variable is incorporated into the reconstructed sliding dynamics to estimate lumped uncertainties and reduce the compensation burden on the robust feedback term. Furthermore, a state-aware adaptive PSO variant combining population-diversity monitoring and differential mutation is developed to jointly tune the 15-dimensional controller parameter vector. The practical finite-time reachability of the sliding variable and the uniform ultimate boundedness of the sliding variable and neural-weight estimation error are analyzed using a Lyapunov framework. Simulation results on a six-degree-of-freedom (6-DOF) robotic arm demonstrate improved tracking accuracy and disturbance-rejection performance, together with reduced high-frequency torque oscillations, compared with the evaluated baseline controllers. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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20 pages, 577 KB  
Article
Adaptive Neural Control for Constrained Biomimetic Rehabilitation Robots Using a Novel High-Order Integral Barrier Function
by Tan Zhang, Jinzhong Zhang and Pianpian Yan
Biomimetics 2026, 11(8), 536; https://doi.org/10.3390/biomimetics11080536 - 2 Aug 2026
Viewed by 92
Abstract
To address the challenges of lumped model uncertainties and tracking error constraints in
biomimetic rehabilitation robot control, this paper proposes a novel high-order integral
barrier function to construct an adaptive neural tracking control scheme. Radial basis
function neural networks (NNs), inspired by the [...] Read more.
To address the challenges of lumped model uncertainties and tracking error constraints in
biomimetic rehabilitation robot control, this paper proposes a novel high-order integral
barrier function to construct an adaptive neural tracking control scheme. Radial basis
function neural networks (NNs), inspired by the receptive field mechanism of motor
neurons, feature local activation and can accurately approximate the nonlinear dynamics
of such bionic rehabilitation devices. Distinct from traditional integral barrier Lyapunov
functions, the presented high-order integral barrier function can accommodate both timevarying
and time-invariant error constraints, while simplifying the controller derivation
and ensuring full differentiability of virtual control laws throughout the backstepping
framework. Supported by the derived barrier function theorems, the tracking error of
the robot is theoretically proven to stay within predefined safe boundaries and converge
exponentially to a compact neighborhood of the origin. Finally, comparative numerical
simulations on a biomimetic rehabilitation robot validate the effectiveness of the proposed
theorem and constrained adaptive neural control strategy Full article
(This article belongs to the Special Issue Bionic Intelligent Robots)
20 pages, 8821 KB  
Article
Numerical Approximation of a Smoking Dynamics Model Using a Hybrid Deep Neural Network Architecture
by Allah Dad, Shumaila Javeed, Mansoor Shaukat Khan, Atif Jameel and Dumitru Baleanu
Math. Comput. Appl. 2026, 31(4), 152; https://doi.org/10.3390/mca31040152 - 2 Aug 2026
Viewed by 159
Abstract
Despite the fact that smoking is still a significant global public health concern, current mathematical models of smoking dynamics primarily depend on conventional numerical solvers. A particular five-compartment smoking dynamics model has not yet been solved using deep neural network (DNN) techniques. In [...] Read more.
Despite the fact that smoking is still a significant global public health concern, current mathematical models of smoking dynamics primarily depend on conventional numerical solvers. A particular five-compartment smoking dynamics model has not yet been solved using deep neural network (DNN) techniques. In order to fill this research gap, this work creates a unique DNN framework that can simulate nonlinear smoking dynamics in a computationally efficient manner. The Levenberg–Marquardt backpropagation technique is used to improve a dual-hidden-layer network consisting of 20 radial basis activation function (RBAF) neurons and 40 log-sigmoid activation function (LSAF) neurons. With a minimum mean squared error (MSE) of 1.865×106 and a coefficient of determination R2 equal to or near unity across all model variables, the trained DNN offers instantaneous predictions while maintaining superior accuracy, in contrast to traditional numerical methods that necessitate the explicit re-solving of differential equations for each parameter change. Crucially, our DNN-based framework is appropriate for automated public health decision-support systems since it functions independently and does not require human intervention during the prediction phase. Key smoking behaviors, such as initiation, quitting efforts, relapse dynamics, and long-term recovery patterns, are successfully replicated by the framework, while relapse dynamics are captured through the recovered-to-potential smoker pathway, consistent with the original model formulation. These findings show that the proposed DNN approach not only closes the methodological gap in the application of deep learning to smoking dynamics but also offers a dependable and computationally effective tool for quick evaluation of intervention scenarios, supporting evidence-based public health decision making without compromising accuracy. Full article
(This article belongs to the Section Natural Sciences)
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29 pages, 7179 KB  
Article
Static Formation Temperature Inversion in Ultra-Deep Wells Based on an IGWO-RBF Surrogate Model
by Wenming Li, Feng Lu, Xu Du, Jianfei Xu, Dali Zhang, Wenjie Jia and Zhengming Xu
Appl. Sci. 2026, 16(15), 7652; https://doi.org/10.3390/app16157652 - 1 Aug 2026
Viewed by 107
Abstract
In ultra-deep well drilling, directly measuring the static formation temperature (SFT) is highly time-consuming, as it requires extended shut-in periods for the wellbore to reach full thermal equilibrium, making it impractical for routine engineering operations. To overcome this challenge, this paper establishes a [...] Read more.
In ultra-deep well drilling, directly measuring the static formation temperature (SFT) is highly time-consuming, as it requires extended shut-in periods for the wellbore to reach full thermal equilibrium, making it impractical for routine engineering operations. To overcome this challenge, this paper establishes a wellbore–formation transient temperature model (WFTM) and proposes an SFT inversion method based on the Improved Grey Wolf Optimizer (IGWO) and Radial Basis Function (RBF) neural network. The RBF network serves as a surrogate model to replace the WFTM during iterative optimization, avoiding the prohibitive computational cost of repeated WFTM evaluations and enabling rapid prediction of the transient wellbore temperature field. Meanwhile, the IGWO algorithm uses the measured bottomhole circulating temperature (BHCT) as a constraint to optimize the geothermal gradient in SFT inversion. Multi-well validation shows that the RBF surrogate predicts BHCT with relative errors consistently below 1%, demonstrating its effectiveness as a substitute for the WFTM. Compared with the direct iterative approach (IGWO-WFTM), the IGWO-RBF method yields slightly lower SFT inversion accuracy, but this deviation remains within engineering tolerances, and the computational time is reduced by approximately 18 times. Requiring only surface temperature and routinely measured BHCT, the proposed approach offers a practical and efficient pathway for real-time assessment of formation temperature during ultra-deep oil well drilling. Full article
(This article belongs to the Special Issue Deep Well Drilling and Sustainable Practices in Petroleum Engineering)
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17 pages, 3008 KB  
Article
Robust Adaptive Dynamic Positioning: An Asynchronous Actor and Critic Approach with Meta-Driven Radial Function Network
by Wanjin Huang, Jiqiang Li and Guoqing Zhang
J. Mar. Sci. Eng. 2026, 14(15), 1420; https://doi.org/10.3390/jmse14151420 - 1 Aug 2026
Viewed by 119
Abstract
Dynamic Positioning systems are crucial for modern marine vessels to maintain positions or track trajectories under environmental disturbances. Traditional model-based and neural network control schemes often suffer from heavy computational burdens, low-velocity nonlinearities, and chattering near decision boundaries during waypoint transitions, which can [...] Read more.
Dynamic Positioning systems are crucial for modern marine vessels to maintain positions or track trajectories under environmental disturbances. Traditional model-based and neural network control schemes often suffer from heavy computational burdens, low-velocity nonlinearities, and chattering near decision boundaries during waypoint transitions, which can trigger actuator saturation. To address these challenges, this paper proposes an enhancing robust adaptive control algorithm. Specifically, a model-free control framework is developed by employing an asynchronous deep Actor–Critic neural network with multi-layer perceptron for high-precision policy approximation in continuous spaces. To accelerate convergence, an online meta-driven radial basis function network is proposed for adaptive reward shaping, optimized by the Adam scheme. Furthermore, at the guidance level, a hysteresis state machine and an adaptive damping reference model are designed to decouple wave-induced high-frequency chattering and eliminate thrust saturation. By applying dynamic surface control, the proposed scheme avoids complex thrust allocation calculations. The proposed method enhances system autonomy and ensures smooth transient behavior while maintaining compatibility with standard marine hardware. Full article
(This article belongs to the Special Issue New Technologies in Autonomous Ship Navigation)
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19 pages, 586 KB  
Article
Prescribed Performance Speed Control Without Initial Condition Restrictions for Asynchronous Motor Drive Systems
by Ruibo Sun, Na Sang, Zhongyu Zhang, Shihang Hu, Zishuo Zhao and Ye Zhang
World Electr. Veh. J. 2026, 17(8), 398; https://doi.org/10.3390/wevj17080398 - 1 Aug 2026
Viewed by 91
Abstract
Asynchronous motors are widely used in electric vehicle drive systems because of their simple structure, low cost, and high reliability. Accurate speed tracking and smooth transient response are important during start-up, acceleration, and deceleration. However, sensing uncertainties and sensor faults may affect the [...] Read more.
Asynchronous motors are widely used in electric vehicle drive systems because of their simple structure, low cost, and high reliability. Accurate speed tracking and smooth transient response are important during start-up, acceleration, and deceleration. However, sensing uncertainties and sensor faults may affect the measured signals and reduce control performance. In this study, an adaptive prescribed performance control (PPC) method is developed for asynchronous motor speed regulation. A nonlinear mapping and an improved tangent-type barrier Lyapunov function (BLF) are used to remove the requirement that the initial tracking error must lie within the prescribed performance bounds. Radial basis function neural networks are used to approximate the unknown nonlinear terms. The stability analysis shows that all closed-loop signals remain bounded and that the tracking error enters and remains within the prescribed performance region after the initial expansion stage. Simulations under different initial motor speeds, the considered sensor-fault conditions, and load disturbances are conducted. Under the adopted comparative conditions, the proposed method reduces the convergence time, steady-state error, maximum tracking error, and recovery time by 69.5%, 93.4%, 92.2%, and 49.4%, respectively. The results show that the proposed method improves the transient response, tracking accuracy, and disturbance recovery of the asynchronous motor drive system. Full article
(This article belongs to the Section Propulsion Systems and Components)
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40 pages, 13940 KB  
Article
Design and Experimental Validation of an ISMC-Based Position Controller with Supervisory RBF Neural Network and PIO for BLDC Motor Systems
by Young Ik Son, Haneul Cho and Junho Kang
Electronics 2026, 15(15), 3373; https://doi.org/10.3390/electronics15153373 - 31 Jul 2026
Viewed by 126
Abstract
This paper proposes a robust position control method that integrates integral sliding mode control (ISMC), a radial basis function neural network (RBF–NN), and a proportional–integral observer (PIO) for a BLDC motor system subject to harmonic-drive loads under nonlinear friction, model uncertainty, and time-varying [...] Read more.
This paper proposes a robust position control method that integrates integral sliding mode control (ISMC), a radial basis function neural network (RBF–NN), and a proportional–integral observer (PIO) for a BLDC motor system subject to harmonic-drive loads under nonlinear friction, model uncertainty, and time-varying disturbances. In the proposed structure, the RBF–NN suppresses the major nonlinear equivalent disturbance components online, while the PIO estimates the residual disturbance remaining after the RBF–NN action. The PIO residual-disturbance estimate is further incorporated into the RBF–NN weight-update law to provide residual-disturbance information to the RBF–NN adaptation and improve the coordination between the two compensation mechanisms. The closed-loop stability of the proposed controller is demonstrated using Lyapunov analysis. The proposed method is validated through comparative simulations using an identified LuGre friction model and hardware experiments under step and sinusoidal reference inputs and disturbances, including baseline and additional-load conditions with increased model uncertainty. The results show that the proposed controller reduces residual tracking errors more effectively than conventional ISMC, ISMC+RBF, and internal model principle (IMP)+PIO controllers without requiring excessive control input, demonstrating its practical robustness in complex BLDC motor drive systems. Full article
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10 pages, 1877 KB  
Proceeding Paper
AI-Driven Shortest-Path Routing Techniques in IoT-Enabled RES-Based EV and Vehicular Networks: A Comprehensive Review of Deep Learning Models
by Balaji Viswanathan, Thoudam Basanta Singh, Brindha Devi Varadharajalu, Maheswari Ellappan and Mutum Bidyarani Devi
Eng. Proc. 2026, 144(1), 14; https://doi.org/10.3390/engproc2026144014 - 31 Jul 2026
Viewed by 99
Abstract
Renewable energy system (RES)-based electric vehicle (EV) charging infrastructure enhances energy security. The need for intelligent routing techniques that achieve low latency, high reliability and adaptive path selection under extremely dynamic traffic situations has increased owing to the quick growth of Internet of [...] Read more.
Renewable energy system (RES)-based electric vehicle (EV) charging infrastructure enhances energy security. The need for intelligent routing techniques that achieve low latency, high reliability and adaptive path selection under extremely dynamic traffic situations has increased owing to the quick growth of Internet of Things (IoT)-enabled vehicular networks. With an emphasis on recurrent neural networks (RNNs), deep belief networks (DBNs), radial basis function neural networks (RBFNNs), and long short-term memory (LSTM) networks, in addition to convolutional neural networks (CNNs), this analysis looks at cutting-edge AI-based models used for shortest-path routing in IoT-driven vehicular ad hoc networks (VANETs). The paper examines how various designs handle issues such as connection instability, heterogeneous sensor data, quick topological changes, and real-time decision making. A comparative analysis shows that DBN and CNN display strong feature learning for intricate mobility patterns and congestion recognition, while sequence-aware techniques like RNN and LSTM advance spatiotemporal traffic estimation. For low-latency route evaluation, RBFNN compromises rapid nonlinear representation. The examination shows that CNN models greatly improve the scalability, adaptability and optimality of routing, confirming AI-enabled structures as a promising path for next-generation IoT-based vehicular routing methods. Full article
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25 pages, 2420 KB  
Article
Fixed-Time Sliding Mode Control of DC-DC Buck Converter with Guaranteed Transient Performance
by Cheng Li, Xinxin Liu, Chaoqun Song, Xinpo Lin, Xiaoning Shen, Yue Zhao, Yabin Gao and Jose I. Leon
Electronics 2026, 15(15), 3253; https://doi.org/10.3390/electronics15153253 - 23 Jul 2026
Viewed by 205
Abstract
The stability and transient performance of DC-DC buck converter output voltage is critical. In order to address the voltage control problem under mismatched disturbances and time-varying output constraints, this paper proposes a voltage control framework of the DC-DC buck converter with the guaranteed [...] Read more.
The stability and transient performance of DC-DC buck converter output voltage is critical. In order to address the voltage control problem under mismatched disturbances and time-varying output constraints, this paper proposes a voltage control framework of the DC-DC buck converter with the guaranteed prescribed performance and fixed stabilization time based on a higher-order fully actuated approach. Firstly, to estimate the mismatched disturbance, a fixed-time extended state observer (ESO) is designed. The original model of buck converter is transformed into a high-order fully actuated system. The uncertainties are approximated by a radial basis function neural network (RBFNN). Then, an adaptive fixed-time sliding mode control law is proposed. The proposed control law could guarantee the prescribed transient performance for the buck converter in the presence of load changing and bounded model uncertainties. The fixed-time stability of the closed-loop system is guaranteed by the Lyapunov approach. The proposed control law is evaluated by comparative experimental tests. Experimental results illustrate the effectiveness and superiority of the proposed control strategy. Full article
(This article belongs to the Special Issue Innovative Technologies in Power Converters, 3rd Edition)
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19 pages, 1468 KB  
Article
Intrinsic Plasticity-Driven Neuroadaptive Asymptotic Tracking Control for a Class of Uncertain Robotic Manipulators
by Qing Chen, Xiangyang Tan, Shuaicheng Hou, Meiyi Qing and Zuojin Li
Sensors 2026, 26(14), 4643; https://doi.org/10.3390/s26144643 - 22 Jul 2026
Viewed by 271
Abstract
This paper proposes a novel neuroadaptive asymptotic tracking control method for a class of uncertain multi-input multi-output (MIMO) robotic manipulators. Firstly, an intrinsic plasticity (IP)-driven cycle echo state network (ESN) is constructed. The intrinsic plasticity mechanism can adaptively adjust neuronal excitability, enhancing the [...] Read more.
This paper proposes a novel neuroadaptive asymptotic tracking control method for a class of uncertain multi-input multi-output (MIMO) robotic manipulators. Firstly, an intrinsic plasticity (IP)-driven cycle echo state network (ESN) is constructed. The intrinsic plasticity mechanism can adaptively adjust neuronal excitability, enhancing the network’s ability to capture complex time-varying dynamics. Meanwhile, the cycle reservoir structure significantly reduces the number of neural connections, thus improving computational efficiency. Secondly, the proposed IP-driven cycle ESN is integrated with the robust integral of the sign of the error (RISE) framework to form a neuroadaptive controller. The IP-driven cycle ESN serves to dynamically approximate the unknown nonlinearities inherent in the robotic system, whereas the RISE term compensates for approximation errors and external disturbances to ensure satisfactory robust performance. Then, a rigorous stability analysis is given to demonstrate that the proposed controller can achieve asymptotic convergence of the tracking error. Finally, simulation experiments are conducted on two typical two-joint manipulators to evaluate the performance of the proposed method. Comparative results demonstrate that, in contrast to the Radial Basis Function Neural Network (RBFNN)-based PI control method, the proposed method achieves faster error convergence rate, higher tracking precision, and smoother control inputs. The results highlight the effectiveness of combining the approximation capability of the IP-driven cycle ESN with the robust compensation capability of the RISE framework for high-precision control of uncertain nonlinear robotic systems. Full article
(This article belongs to the Section Sensors and Robotics)
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17 pages, 11389 KB  
Article
Experimental Study and Numerical Simulation on Anti-Scouring Performance of 3D Ecological Protection Mat for Slope Protection
by Ming Huang, Yunhao Chu, Kang Liu and Fan Yang
Coatings 2026, 16(7), 832; https://doi.org/10.3390/coatings16070832 - 13 Jul 2026
Viewed by 276
Abstract
As an innovative ecological material widely adopted for surface protection of hydraulic soil–cement slope composites, 3D ecological slope protection mats remain insufficiently studied in terms of their anti-scour capacity under hydrodynamic erosion. This work combines physical model tests and numerical simulations to investigate [...] Read more.
As an innovative ecological material widely adopted for surface protection of hydraulic soil–cement slope composites, 3D ecological slope protection mats remain insufficiently studied in terms of their anti-scour capacity under hydrodynamic erosion. This work combines physical model tests and numerical simulations to investigate its scour resistance, and adopts a radial basis function (RBF) neural network-based intelligent inversion method to calibrate numerical model parameters. Physical test results demonstrate that longer vegetation growing periods effectively strengthen slope anti-scouring performance. At 2 m/s flow velocity, extending the growth period from 2 months to 3 and 4 months increases bed shear stress of 3D ecological protection mat specimens by 41% and 19%, reduces soil loss by 49% and 33%, and decreases scour depth by 23% and 13%. Both scour depth and soil loss rise rapidly initially before leveling off, with larger ultimate values under higher flow velocities. The established numerical model achieves a 3.1% relative error between inverted and measured data, proving high inversion accuracy. Simulations under 1~5 m/s flow velocities reveal that flow velocity decreases significantly over the protected slope, and scour depth and scouring area expand gradually with increasing flow velocity. Full article
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19 pages, 3110 KB  
Article
Long-Term GNSS Satellite Clock Error Forecasting Using Inter-Satellite Comparison Data and RBF Neural Networks
by Tieqiang Liu, Guocheng Wang, Li Liu, Yin Huang, Lintao Liu, Zhiwu Cai, Yu Xiao, Mingyuan Liu and Jianguo Wang
Appl. Sci. 2026, 16(14), 6939; https://doi.org/10.3390/app16146939 - 10 Jul 2026
Viewed by 215
Abstract
Accurate long-term prediction of GNSS satellite clock errors is essential for autonomous navigation, real-time precise point positioning (PPP), and continuous positioning, navigation, and timing (PNT) services when real-time clock products are unavailable or delayed. However, conventional methods, such as quadratic polynomial fitting and [...] Read more.
Accurate long-term prediction of GNSS satellite clock errors is essential for autonomous navigation, real-time precise point positioning (PPP), and continuous positioning, navigation, and timing (PNT) services when real-time clock products are unavailable or delayed. However, conventional methods, such as quadratic polynomial fitting and Kalman filtering, have limited capability in modeling nonlinear and non-stationary clock behaviors over long prediction intervals, especially under abnormal onboard atomic clock conditions. To address this issue, an inter-satellite comparison data (ISCD)-based radial basis function neural network (RBFNN) model is proposed for long-term satellite clock error prediction. Through correlation analysis, reference satellite clocks closely related to the target satellite are selected, and both ISCD and satellite-ground comparison data are integrated to establish a nonlinear prediction model. Experiments using GPS and Galileo satellite clock datasets demonstrate that the proposed method significantly improves long-term prediction accuracy. For 180-day prediction, the proposed model reduces the RMSE by more than 60% for GPS satellites and approximately 99% for Galileo satellites with abnormal clock behavior compared with conventional methods. Rolling prediction experiments further verify the robustness and stability of the proposed model. Full article
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27 pages, 8157 KB  
Article
An Enhanced Particle Swarm Optimized RBF Model for Precise Fish Population Estimation in Cage Farming
by Gang Yang, Xuelei Wang, Junping Wang, Weiliang Shen, Hongsheng Yang, Qingfei Li and Chenggang Lin
Animals 2026, 16(13), 2057; https://doi.org/10.3390/ani16132057 - 3 Jul 2026
Viewed by 330
Abstract
In cage aquaculture, precise estimation of fish biomass is critically important for determining appropriate feeding strategies and evaluating production capacity. Currently, prevailing fish counting approaches heavily rely on acoustic or optical technologies. However, the accuracy and reliability of the obtained data are largely [...] Read more.
In cage aquaculture, precise estimation of fish biomass is critically important for determining appropriate feeding strategies and evaluating production capacity. Currently, prevailing fish counting approaches heavily rely on acoustic or optical technologies. However, the accuracy and reliability of the obtained data are largely compromised by factors such as fish occlusion and water turbidity in practical cage farming environments. To address this limitation, this study proposed a novel method for estimating fish population size deduced from dynamic feeding information, based on the model integrated environmental and biological factors, feed intake and biomass. A 10-week feeding experiment was carried out to collect multidimensional data including feed intake, growth parameters, and environmental variables to construct a dataset correlating feeding amount with primary influential factors. Herein a bioenergetics-informed radial basis function neural network, optimized via particle swarm optimization (BE-PSO-RBF), was developed based on those empirical data. Model validation using 47 independent test samples showed that the hybrid model achieved a mean absolute error (MAE) of 26.82, a root mean square error (RMSE) of 35.62, and a mean absolute percentage error (MAPE) of 4.14%, confirming its robust generalization performance. These findings suggest that feed-intake-based population estimation may provide a feasible complementary approach for fish population assessment under cage farming conditions similar to those investigated in this study. Full article
(This article belongs to the Section Aquatic Animals)
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26 pages, 1467 KB  
Article
Adaptive Neural Network Preset-Time Control for RDDV with Unknown Dynamics
by Mengjie Wang, Kou Du, Ximing Cai, Shuai Li, Qian Qin, Yayun Zhang, Jinjie Gan, Lianhua Wang, Peiguo Zhang, Jichun Chen, Jianyong Yao and Xiaowei Yang
Electronics 2026, 15(13), 2915; https://doi.org/10.3390/electronics15132915 - 3 Jul 2026
Viewed by 315
Abstract
This paper addresses the high-precision position tracking control problem for the rotary direct-drive valve (RDDV) subject to complex nonlinear dynamics and unknown external disturbances. To achieve superior transient and steady-state performance, a novel adaptive neural network preset-time control (ANNPTC) strategy is proposed. Distinct [...] Read more.
This paper addresses the high-precision position tracking control problem for the rotary direct-drive valve (RDDV) subject to complex nonlinear dynamics and unknown external disturbances. To achieve superior transient and steady-state performance, a novel adaptive neural network preset-time control (ANNPTC) strategy is proposed. Distinct from conventional finite-time or fixed-time control schemes, the proposed ANNPTC ensures that the tracking error converges to a prescribed neighborhood of the origin within a prescribed residual set after the user-defined time Tc under the admissible initial condition. Specifically, adaptive radial basis function neural networks (RBFNNs) are utilized to estimate and compensate for unmodeled dynamics and disturbances, significantly enhancing the steady-state precision of the system. The uniform ultimate boundedness of all signals in the closed-loop system and the prescribed-performance property are established via Lyapunov stability analysis. Finally, extensive simulation results on a high-fidelity RDDV model demonstrate that the proposed method yields faster response speed and higher tracking accuracy compared with benchmark controllers, thereby validating its efficacy and superiority in RDDV applications. Full article
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20 pages, 19624 KB  
Article
An Enhanced Physics-Informed Neural Network with Spatial RBF Embedding and Temporal Initial Condition Embedding for the Allen–Cahn Equation
by Zhiwen Wang and Minxin Chen
Mathematics 2026, 14(13), 2344; https://doi.org/10.3390/math14132344 - 2 Jul 2026
Viewed by 346
Abstract
Phase field models are widely employed in materials science, fluid dynamics, fracture mechanics, and image processing to describe physical processes involving complex interface evolution, with the Allen–Cahn equation serving as a classic example. Physics-informed neural networks (PINNs) have been extensively applied to various [...] Read more.
Phase field models are widely employed in materials science, fluid dynamics, fracture mechanics, and image processing to describe physical processes involving complex interface evolution, with the Allen–Cahn equation serving as a classic example. Physics-informed neural networks (PINNs) have been extensively applied to various partial differential equations, but their accuracy in solving the Allen–Cahn equation is often compromised due to the sharp variations of the equation’s solution across phase interfaces. This paper proposes an enhanced PINN with spatial and temporal feature embedding strategies (STFE-PINN) for solving the Allen–Cahn equation. Specifically, for the spatial embedding, the input spatial coordinates are passed through a radial basis function (RBF) neural network, and its output is embedded as a feature into the PINN. By incorporating learnable shape parameters, the RBF embedding adaptively adjusts its basis functions, which strengthens the PINN’s ability to capture high-frequency spatial features and steep gradients. For the temporal embedding, the initial condition is embedded as an additional feature. This strategy enables the network to retain the information of the initial condition throughout training, thereby improving the learning of the phase field evolution and enhancing the accuracy of the PINN. Numerical experiments in one, two, and three dimensions validate the effectiveness and stability of the proposed method. Full article
(This article belongs to the Special Issue New Advances in Physics-Informed Machine Learning)
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