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22 pages, 1472 KB  
Article
Robust Secrecy-Aware Power Allocation for UAV-Assisted IoT Sensing Networks Under Worst-Case Eavesdropping
by Mohammad Ahmed Alnakhli
Electronics 2026, 15(13), 2968; https://doi.org/10.3390/electronics15132968 - 7 Jul 2026
Abstract
We investigate secure data transmission in a unmanned aerial vehicle (UAV)-assisted Internet of Things (IoT) sensing network, focusing on maximizing multi-sensor uplink secrecy capacity under practical power constraints and severe co-channel interference. Due to the coupled signal-to-interference-plus-noise ratio (SINR) expressions and the non-smooth [...] Read more.
We investigate secure data transmission in a unmanned aerial vehicle (UAV)-assisted Internet of Things (IoT) sensing network, focusing on maximizing multi-sensor uplink secrecy capacity under practical power constraints and severe co-channel interference. Due to the coupled signal-to-interference-plus-noise ratio (SINR) expressions and the non-smooth secrecy-rate function, the formulated power allocation problem is highly nonconvex and mathematically challenging. To efficiently solve this problem, we exploit a novel mathematical reformulation by introducing a smooth approximation of the secrecy metric and developing a computationally efficient optimization framework based on sequential quadratic programming (SQP) with analytically derived gradients. The main strength of this framework lies in its low-complexity, deterministic nature, which eliminates the need for computationally exhaustive search heuristics while guaranteeing fast, stable convergence to a Karush–Kuhn–Tucker (KKT) point. Furthermore, we incorporate a robust worst-case eavesdropper modeling approach to guarantee secure communication under severe adversarial conditions. Numerical results demonstrate that the proposed method significantly improves sum secrecy performance compared to conventional equal-power and baseline allocation schemes, proving highly scalable for real-time data collection in environmental monitoring, smart cities, and surveillance applications. Full article
(This article belongs to the Section Microwave and Wireless Communications)
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15 pages, 5493 KB  
Article
Optical Mask Generation Based on State-Switching Dynamics for Time-Delay Reservoir Computing
by Tong Zhao, Tianpei Cui, Baofeng Feng, Zhimin Bai, Pengfa Chang, Lijun Qiao, Su Yan and Xiaopeng Fan
Photonics 2026, 13(7), 641; https://doi.org/10.3390/photonics13070641 - 1 Jul 2026
Viewed by 179
Abstract
In time-delay reservoir computing (TDRC), mask signal generation techniques in the input layer remain a key factor limiting system integration. In this study, we propose an optical mask generation scheme based on steady–quasi-periodic state switching (S-QPS) dynamics in a semiconductor laser with optical [...] Read more.
In time-delay reservoir computing (TDRC), mask signal generation techniques in the input layer remain a key factor limiting system integration. In this study, we propose an optical mask generation scheme based on steady–quasi-periodic state switching (S-QPS) dynamics in a semiconductor laser with optical feedback. Experimentally generated S-QPS signals are applied to a TDRC system as mask signals, and the system performance is evaluated using the Santa Fe chaotic time-series prediction task. S-QPS signals are numerically generated based on the Lang–Kobayashi rate equations. The optimal normalized mean square error is 0.027. An analysis of the factors affecting system performance is carried out. The results indicate that period offset has a limited impact on system performance. In contrast, noise-induced amplitude fluctuations have a more pronounced impact. These results provide insights into the use and optimization of S-QPS signals for optical mask generation in TDRC systems. Full article
(This article belongs to the Special Issue Advanced Lasers and Their Applications, 3rd Edition)
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26 pages, 12501 KB  
Article
An IR-RIME-SQP-Based Spectrum Modification Method for Shallow Surface Electromagnetic Detection Transmitting Scheme of Metal Traps in Forested Areas
by Zeyu An, Xiaoyue Fan, Yuhang Wang and Tao Zhang
Sensors 2026, 26(13), 4032; https://doi.org/10.3390/s26134032 - 25 Jun 2026
Viewed by 179
Abstract
In the electromagnetic detection of shallow subsurface metal snaring traps in forested areas, conventional transmission schemes such as square waves, PRBS and PSO waveforms inevitably excite severe clutter in soils exhibiting viscous remanent magnetization (VRM), which drastically degrades the signal-to-clutter ratio (SCR). To [...] Read more.
In the electromagnetic detection of shallow subsurface metal snaring traps in forested areas, conventional transmission schemes such as square waves, PRBS and PSO waveforms inevitably excite severe clutter in soils exhibiting viscous remanent magnetization (VRM), which drastically degrades the signal-to-clutter ratio (SCR). To resolve this issue, this paper proposes a spectrum modification method for the transmitting scheme based on an Interval Robust hybrid RIME and Sequential Quadratic Programming (IR-RIME-SQP) algorithm. By coupling the Debye relaxation characteristics of ferromagnetic targets with the soil VRM model, the proposed method concentrates limited transmission energy into a bell-shaped frequency window near the target’s characteristic frequency. Furthermore, interval analysis is introduced to ensure robust performance against the dynamic drift of coil parameters. The feasibility of this novel transmitting scheme is validated through ablation experiments and comparative simulations. Finally, laboratory measurements demonstrate that IR-RIME-SQP provides a more rational and efficient energy allocation strategy, improving the targeted frequency energy retention (TFER) by approximately 16.4% and thereby enhancing both detection efficiency and precision. Full article
(This article belongs to the Section Electronic Sensors)
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15 pages, 1218 KB  
Article
Hybrid NMPC-ESO-PINSE Approach for Liquid Level Control in a Nonlinear Four-Tank System: Integration of Deep Learning and Extended State Observation Under Stochastic Uncertainties
by Zohra Zidane, El Mostafa Atify, Mohammed Zidane and Ahmed Boumezzough
Automation 2026, 7(3), 98; https://doi.org/10.3390/automation7030098 - 18 Jun 2026
Viewed by 164
Abstract
Liquid storage tanks are widely used in sectors such as water treatment, oil and gas, food processing, and chemical manufacturing. Knowing the exact amount of liquid in a tank is essential for ensuring safety, preventing spills, and optimizing process control; therefore, the liquid [...] Read more.
Liquid storage tanks are widely used in sectors such as water treatment, oil and gas, food processing, and chemical manufacturing. Knowing the exact amount of liquid in a tank is essential for ensuring safety, preventing spills, and optimizing process control; therefore, the liquid level in a tank must be maintained at a precise reference point. This is where liquid level control for tanks becomes crucial and constitutes a fundamental problem in the industrial sector due to nonlinearities, multivariable coupling, and stochastic disturbances. Given the drawbacks of available control methods, such as classical Model Predictive Control (MPC), which are highly dependent on model accuracy and struggle to reject complex stochastic noise, predicting random disturbances represents a major technological challenge. A new approach is proposed to specifically address the problem and challenge of the four-tank system, where water levels in two lower tanks must be controlled by two pumps, often with varying delays and significant parameter disturbances. To establish a relationship between expected performance and MPC parameters, this approach uses a novel hybrid nonlinear MPC, Extended State Observer, and Physics-Informed Neural State Estimation (NMPC-ESO-PINSE) architecture. A Physics-Informed Neural State Estimation (PINSE) layer, chosen for its learning capacity, is designed to filter sensor noise by applying Bernoulli’s physical laws, while an Extended State Observer (ESO) is integrated to capture and compensate for unmodeled uncertainties in the process. Finally, a proposed hybrid (NMPC-ESO-PINSE) strategy leverages these clean, physically consistent state estimations to solve a non-convex optimization problem via Sequential Quadratic Programming (SQP), computing optimal pump voltages. Extensive numerical simulations demonstrate the superior resilience of this decoupled framework against parametric drifts and continuous noise sequences, yielding a +27.36% reduction in global Root Mean Square Error (RMSE) compared to standard NMPC, accelerating the closed-loop settling time to 15.2 s, and restricting transient overshoot to just 0.18%. Full article
(This article belongs to the Special Issue Robust Estimation and Control of Uncertain Nonlinear Systems)
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21 pages, 1972 KB  
Article
Feedforward Neural Network-Based MPC Optimized by Hybrid Fractional PSO–SQP for Trajectory Tracking of Autonomous Vehicles
by Fahad Alotaibi, Habib Dhahri, Saleh Almohaimeed and Awais Mahmood
Automation 2026, 7(3), 95; https://doi.org/10.3390/automation7030095 - 15 Jun 2026
Viewed by 318
Abstract
Background/Objective: Autonomous vehicles (AVs) require control algorithms capable of handling complex and dynamic environments while satisfying multiple conflicting objectives such as safety, comfort, energy efficiency, and trajectory accuracy. Model predictive control (MPC) offers a principled framework for multi-constraint optimization, yet its real-time feasibility [...] Read more.
Background/Objective: Autonomous vehicles (AVs) require control algorithms capable of handling complex and dynamic environments while satisfying multiple conflicting objectives such as safety, comfort, energy efficiency, and trajectory accuracy. Model predictive control (MPC) offers a principled framework for multi-constraint optimization, yet its real-time feasibility remains challenging for nonlinear vehicle dynamics. Methods: This paper presents a feedforward neural network (FNN)-based MPC framework for autonomous vehicle trajectory tracking. The FNN approximates the coupled vehicle dynamics and visual preview error model using an algebraic sum of log-sigmoid functions. Three adaptive FNN parameter sets, namely, the scaling factor, convergence parameter, and time-shifting parameter, are jointly optimized using a hybrid algorithm that combines the global search capability of fractional particle swarm optimization (FPSO) with the local refinement of sequential quadratic programming (SQP). Results: Comprehensive scenario-based simulations are performed to evaluate trajectory tracking dynamics under dry conditions with an adhesion coefficient of 0.8 and a vehicle mass of 1723 kg moving at a speed of 80 km/h. The results are quantitatively compared with a traditional PID controller and a structurally comparable MPC framework from the literature under identical simulation conditions; related DRL- and RL-based methods are discussed qualitatively for contextual orientation only. The stability, reliability, and computational complexity of the proposed framework are examined based on the mean square error, fitness value, and computational budget in GFLOPs for 100 independent runs. Conclusions: The proposed FNN-based MPC framework demonstrates improved tracking accuracy and optimizer reliability in simulation. While the present results indicate promising computational behavior, real-time deployment will require further validation on embedded automotive hardware and under closed-loop real-time constraints. Full article
(This article belongs to the Special Issue AI-Enhanced Measurement and Control for Robotic Systems)
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19 pages, 2236 KB  
Article
GRU-Based Online PID Gain Scheduling Enhanced by High-Quality Dataset Construction
by Xinhao Zhao, Zhaopeng Dong, Tao Zhu and Jiayi Zhu
Appl. Sci. 2026, 16(12), 6032; https://doi.org/10.3390/app16126032 - 15 Jun 2026
Viewed by 152
Abstract
To address the limited adaptability of fixed-parameter PID controllers under dynamically varying reference signals and the strong dependence of data-driven PID methods on training-data quality, this paper proposes a GRU-based online PID gain-scheduling framework supported by high-quality dataset construction. Diverse reference excitations are [...] Read more.
To address the limited adaptability of fixed-parameter PID controllers under dynamically varying reference signals and the strong dependence of data-driven PID methods on training-data quality, this paper proposes a GRU-based online PID gain-scheduling framework supported by high-quality dataset construction. Diverse reference excitations are first designed, and sequential quadratic programming (SQP) is used as an expert label generator to produce trajectory-level PID gain labels. A region-of-interest (ROI)-based dynamic sample selection strategy is then introduced to retain informative transient samples and reduce the dominance of redundant steady-state data. The gated recurrent unit (GRU) network learns a temporal mapping from error-state sequences to PID gains and is deployed online with closed-loop safeguards, including filtered derivative information, gain denormalization, smoothing, and actuator constraints. In a representative nominal neural-controller benchmark, GRU-PID achieves a rise time of 0.59 s, a settling time of 0.97 s, ISE = 2.10, ITAE = 39.35, and TV = 394.48, showing a favourable balance between tracking accuracy and control-signal smoothness. Five-seed tests further indicate that GRU-PID provides stable nominal performance comparable to competitive neural schedulers, while simulation-based robustness evaluations suggest lower tracking errors than the tested neural baselines under measurement noise, step disturbance, actuator saturation, and combined uncertainty scenarios within the considered benchmark setting. Full article
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31 pages, 26232 KB  
Article
Magnetic Composites for Advanced Characterization of Magnetic Field Sensors and Biosensors
by Ekaterina A. Burban, Alexander P. Safronov, Ksenia O. Il’inova, Grigory Yu. Melnikov, Andrey V. Svalov, Igor V. Beketov, Anton A. Yushkov and Galina V. Kurlyandskaya
Sensors 2026, 26(12), 3794; https://doi.org/10.3390/s26123794 - 14 Jun 2026
Viewed by 427
Abstract
Gadolinium is a rare-earth element that is promising for the field of biomedicine due to its unique properties that enhance image quality, giving it high potential in targeted cancer therapy, antimicrobial treatments, etc. The disadvantage of Gd-containing materials is their high toxicity. In [...] Read more.
Gadolinium is a rare-earth element that is promising for the field of biomedicine due to its unique properties that enhance image quality, giving it high potential in targeted cancer therapy, antimicrobial treatments, etc. The disadvantage of Gd-containing materials is their high toxicity. In this work, ensembles of Fe and Al2O3 nanoparticles were fabricated by the electric explosion of wire and Gd ribbons using rapid quenching techniques. Stable Fe, Fe/Gd and Fe/Gd/Al2O3 aqueous suspensions with a Z-potential of about −54 mV were fabricated by the ball-milling mechanosynthesis of Fe (100%), Fe and Gd (70 and 30 wt. % accordingly) and Fe, Al2O3, and Gd (69, 30 and 1 wt.% accordingly). Fillers from suspensions were used for the synthesis of epoxy composites mimicking natural tissue with embedded magnetic particles. The concentration range for synthesized epoxy composites (0, 5, 10, and 15 wt.% of the filler) corresponded to the biomedical range of interest. Thin-film magnetoimpedance (MI) elements were prepared by a sputtering technique: conventional [FeNi/Cu]5/Cu/[Cu/FeNi]5 (NP) element and [FeNi/Cu]5/Cu/[Cu/P{FeNi]5} element with patterned top multilayer (SqP). They showed a maximum MI ratio of about 160% for NP and about 60% for SqP. MI sensor response was affected by the presence of filled magnetic composites in the shape of cylinders (5 mm × 4 mm) situated at about 1 mm due to the stray fields in the filler. MI response showed a linear dependence on the filler concentration for each selected position. These results open the possibility to develop new iron- and gadolinium-containing materials for simultaneous magnetic imaging and detection by magnetic field sensors, extending the functional properties of Fe/Gd materials for biomedical devices and therapies. Full article
(This article belongs to the Section Sensor Materials)
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21 pages, 3695 KB  
Article
Joint Position–Orientation Deployment Design of UAV-Borne Linear-Array Angle-of-Arrival Sensors for Target UAV Localization
by Jiawei Tang, Tian Chang, Haiqi Liu, Zhe Yu, Dekang Liu and Xuhui Ding
Drones 2026, 10(6), 446; https://doi.org/10.3390/drones10060446 - 7 Jun 2026
Viewed by 242
Abstract
This paper investigates joint deployment of unmanned aerial vehicle (UAV)-borne linear-array angle-of-arrival (AOA) sensors for localizing a target UAV in three-dimensional space. Since each sensing UAV carries a lightweight one-dimensional (1-D) AOA array, each measurement provides only one angular constraint, and its information [...] Read more.
This paper investigates joint deployment of unmanned aerial vehicle (UAV)-borne linear-array angle-of-arrival (AOA) sensors for localizing a target UAV in three-dimensional space. Since each sensing UAV carries a lightweight one-dimensional (1-D) AOA array, each measurement provides only one angular constraint, and its information contribution depends jointly on the UAV waypoint and array pointing direction. This leads to a coupled coordinate–orientation design problem that differs from conventional full-AOA deployment. We formulate a Cramér–Rao lower bound (CRLB)-based framework under A- and D-optimality criteria, covering both free-flight and constrained hovering regions. By exploiting the structure of the 1-D AOA Fisher information matrix, we show that, for fixed UAV coordinates, the orientation block can be exactly eliminated through a low-dimensional eigenproblem. The resulting reduced coordinate problem is then solved by a geometry-structured sequential quadratic programming (SQP) method, whose curvature model captures the radial and tangential sensitivities induced by line-of-sight geometry. Numerical simulations further validate the effectiveness of the proposed approach. Full article
(This article belongs to the Section Drone Communications)
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46 pages, 3292 KB  
Article
Autonomous Fault-Tolerant Cooperative Tracking and Obstacle Avoidance for UAV Swarm in Complex Maritime Environments
by Zhiyang Zhang, Xiaolong Liang, Aoyu Zheng and Ning Wang
Drones 2026, 10(5), 388; https://doi.org/10.3390/drones10050388 - 19 May 2026
Viewed by 313
Abstract
To address the challenge of stable tracking of moving maritime targets by unmanned aerial vehicle(UAV) swarm in environments with threat zones and platform failure risks, this paper proposes a cooperative tracking and guidance strategy integrating Distributed Model Predictive Control (DMPC) with Sequential Quadratic [...] Read more.
To address the challenge of stable tracking of moving maritime targets by unmanned aerial vehicle(UAV) swarm in environments with threat zones and platform failure risks, this paper proposes a cooperative tracking and guidance strategy integrating Distributed Model Predictive Control (DMPC) with Sequential Quadratic Programming (SQP). A cooperative tracking model is developed incorporating UAV kinematics, environmental threats, stereo-vision positioning, and field-of-view constraints. Two original strategies are introduced within the DMPC framework: an altitude-cooperative target recapture strategy reduces target total loss duration by approximately 7 s compared to fixed-altitude baselines, while a distributed formation reconfiguration strategy restores stable tracking within 10 s after member failure and ensures safe inter-UAV separation. A multi-constraint trajectory tracking controller based on DMPC-SQP achieves real-time co-optimization of threat avoidance, formation maintenance, and tracking accuracy. Simulation results in dense threat environments demonstrate a 93.4% Quadratic Programming feasibility rate, with mean tracking error reduced by 25.4% over fixed-altitude DMPC and 48.7% over methods based on the Linear Quadratic Regulator (LQR), while maintaining robust performance under 300 ms communication delay, sensor noise, and moderate wind disturbance. Full article
(This article belongs to the Special Issue Flight Control and Collision Avoidance of UAVs: 2nd Edition)
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29 pages, 6537 KB  
Article
Multi-Objective Trajectory Optimization Method for Connected Autonomous Vehicles Based on Risk Potential Field
by Kedong Wang, Dayi Qu, Ziyi Yang, Yuxiang Yang and Shanning Cui
Mathematics 2026, 14(9), 1415; https://doi.org/10.3390/math14091415 - 23 Apr 2026
Viewed by 292
Abstract
The planning of trajectories for Connected Autonomous Vehicles (CAVs) represents a pivotal aspect of autonomous driving technologies, enabling secure navigation within traffic environments. Traditional models for trajectory control primarily focus on the efficiency and safety of individual vehicles but often overlook the dynamics [...] Read more.
The planning of trajectories for Connected Autonomous Vehicles (CAVs) represents a pivotal aspect of autonomous driving technologies, enabling secure navigation within traffic environments. Traditional models for trajectory control primarily focus on the efficiency and safety of individual vehicles but often overlook the dynamics involved in vehicle-to-vehicle and vehicle-to-infrastructure interactions. This study introduces a novel concept, the “driving risk field,” which imposes constraints on vehicular movement within designated road spaces to enhance safety. A vehicle dynamics model is developed, employing a non-linear fifth-degree polynomial to approximate the trajectory curves, with optimization performed using the Sequential Quadratic Programming (SQP) method. The efficacy of the optimized model is validated through simulations on the Prescan/Simulink platform, demonstrating a 17.9% reduction in trajectory angle slopes and a 23.4% decrease in lateral and longitudinal errors compared to conventional Model Predictive Control (MPC), Pure-Pursuit (PP) and Linear Quadratic Regulator (LQR) models. This approach significantly enhances vehicle control in traffic bottleneck areas, indicating superior trajectory adaptation. Full article
(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems, 2nd Edition)
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18 pages, 7394 KB  
Article
Stability and Optimization of a Vector Thrust-Controlled Tail-Sitter UAV Based on Flight Test
by Ruishuo Li, Xiaowen Shan and Hao Wang
Drones 2026, 10(5), 316; https://doi.org/10.3390/drones10050316 - 22 Apr 2026
Viewed by 624
Abstract
Stability plays essential roles for Vertical Take-Off and Landing (VTOL) vehicles. This paper investigates the stability characteristics of a novel tail-sitter VTOL vehicle employing vector thrust control, specifically focusing on nonlinear modeling and parameter optimization. Firstly, the tail-sitter VTOL which employs vector thrust [...] Read more.
Stability plays essential roles for Vertical Take-Off and Landing (VTOL) vehicles. This paper investigates the stability characteristics of a novel tail-sitter VTOL vehicle employing vector thrust control, specifically focusing on nonlinear modeling and parameter optimization. Firstly, the tail-sitter VTOL which employs vector thrust controlling principles, is designed, and manufactured using 3D printing and carbon-fiber reinforced techniques, with a customized flight controller implemented on the PX4 architecture. To address the nonlinear dynamic characteristics introduced by the vector thrust mechanism, a nonlinear dynamic model for cruise flight is established based on an offline database and validated against cruise flight test data. Flight tests show that the vector-thrust-based pitch control provides rapid response and accurate tracking during cruise flight. Furthermore, based on the validated model, a hybrid optimization strategy combining pattern search and sequential quadratic programming (SQP) is used to tune the cascaded control parameters. Simulation results demonstrate that the optimized controller reduces the rise time from 6.8 s to 0.2 s and the settling time from 10.1 s to 0.9 s under the tested cruise-condition step response, indicating a marked improvement in dynamic response performance. This study provides a practical framework for cruise-flight modeling, pitch-stability analysis, and control-parameter optimization of vector-thrust tail-sitter UAVs. Full article
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26 pages, 3386 KB  
Article
A Two-Level Optimal Water Allocation Model for Canal-Drip Irrigation Systems Based on Decomposition–Coordination Theory
by Jingzheng Li, Chunfang Yue and Shengjiang Zhang
Sustainability 2026, 18(7), 3217; https://doi.org/10.3390/su18073217 - 25 Mar 2026
Viewed by 556
Abstract
Agriculture in Xinjiang, a region in arid northwest China, is almost entirely dependent on irrigation, leading to significant supply–demand contradictions. This study addresses the spatial and temporal mismatches between water supply and demand, and the resulting conflicts in crop water supply. Using the [...] Read more.
Agriculture in Xinjiang, a region in arid northwest China, is almost entirely dependent on irrigation, leading to significant supply–demand contradictions. This study addresses the spatial and temporal mismatches between water supply and demand, and the resulting conflicts in crop water supply. Using the primary irrigation cycle of Wutai branch canal as a case study, we developed a two-level optimal water allocation model based on large-scale system optimization. For the lateral canal water distribution, a model minimizing the sum of squares of the water shortage rate was solved using the Sequential Quadratic Programming (SQP) algorithm. For the drip irrigation systems, water distribution time was incorporated as a second objective, and the resulting bi-objective model was solved using the Non-dominated Sorting Genetic Algorithm II (NSGA-II). Compared to actual distribution processes, our results show that (1) 74% of the distribution canals and pipelines achieved over 90% of their design flow rate, fully utilizing flow capacity and reducing the overall distribution time of the branch canal by 4.68 h. (2) The overall water shortage rate was reduced by 1.59% compared to the actual rate, with a more balanced water allocation among users. These results demonstrate that the model can effectively coordinate water distribution in a multi-level canal system, enhance the fairness of water use, and provide a valuable reference for single-event water distribution in water-scarce areas. Full article
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28 pages, 2201 KB  
Article
Addressing Mixed-Integer Nonlinear Energy Management in Hybrid Vehicles: Comparing Genetic Algorithm and Sequential Quadratic Programming Within Model Predictive Control
by Ferris Herkenrath, Silas Koßler, Marco Günther and Stefan Pischinger
Energies 2026, 19(6), 1535; https://doi.org/10.3390/en19061535 - 20 Mar 2026
Viewed by 519
Abstract
Model Predictive Control (MPC) has emerged as a promising approach for energy management in hybrid electric vehicles, enabling predictive optimization of powertrain operation. The energy management problem in parallel hybrid powertrains constitutes a Mixed-Integer Nonlinear Programming (MINLP) problem, combining continuous decision variables such [...] Read more.
Model Predictive Control (MPC) has emerged as a promising approach for energy management in hybrid electric vehicles, enabling predictive optimization of powertrain operation. The energy management problem in parallel hybrid powertrains constitutes a Mixed-Integer Nonlinear Programming (MINLP) problem, combining continuous decision variables such as torque distribution with discrete decisions including engine on/off states and clutch engagement. This problem structure presents distinct challenges for different optimization approaches. Gradient-based methods such as Sequential Quadratic Programming (SQP) solve continuous, differentiable optimization problems and require auxiliary methods to handle integer variables, while metaheuristic approaches such as Genetic Algorithms (GA) can handle the mixed-integer structure directly at the cost of increased computational effort. This study presents a systematic comparison between GA and SQP as optimization solvers within an MPC framework for a P1P3 parallel hybrid powertrain. A multi-objective cost function is formulated to simultaneously optimize system efficiency, battery state of charge management, and noise emissions. Both approaches are evaluated across the WLTC as well as a real-world RDE scenario. On the WLTC, both MPC approaches reduce fuel consumption by 0.5–1.0% and improve system efficiency by 3.7–4.6% compared to a state-of-the-art deterministic reference strategy optimized for fuel consumption. At the same time, both approaches additionally achieve substantial reductions in noise emissions compared to the deterministic reference, which was not optimized for acoustic behavior. On both cycles, the GA-based MPC achieves favorable performance compared to SQP, with the performance gap widening from the WLTC to the RDE cycle. Both methods achieve real-time capability, yet SQP reduces computational time by a factor of four compared to GA. As long as computational resources in automotive ECUs remain constrained, this efficiency advantage positions gradient-based optimization for series production applications, whereas metaheuristic methods offer greater flexibility for concept development stages with relaxed real-time requirements. The findings contribute to the understanding of optimization algorithm selection for MINLP energy management problems in hybrid electric vehicles. Full article
(This article belongs to the Special Issue Challenges and Research Trends of Energy Management)
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37 pages, 41641 KB  
Article
Bumpless Multi-Mode Control Allocation for Over-Actuated AUV Docking
by Peiyan Gao, Yiping Li, Gaopeng Xu, Yuexing Zhang, Junbao Zeng, Yiqun Wang and Shuo Li
J. Mar. Sci. Eng. 2026, 14(5), 516; https://doi.org/10.3390/jmse14050516 - 9 Mar 2026
Viewed by 588
Abstract
This paper addresses the multi-phase homing and docking missions of over-actuated autonomous underwater vehicles (AUVs), where switching among forward cruising, reverse braking, and hovering can induce actuator saturation, rate limit violations, and undesirable transients. We propose a unified framework that couples supervisory mode [...] Read more.
This paper addresses the multi-phase homing and docking missions of over-actuated autonomous underwater vehicles (AUVs), where switching among forward cruising, reverse braking, and hovering can induce actuator saturation, rate limit violations, and undesirable transients. We propose a unified framework that couples supervisory mode management with mode-driven constrained control allocation solved by a warm-started sequential quadratic programming (SQP) routine. The controllable wrench is modeled by a mode-dependent differentiable map constructed from the actuator models, and the allocator enforces amplitude bounds and per-cycle increment limits while trading off wrench tracking and actuator usage through mode-scheduled weights. To mitigate switching transients, a continuous transition factor is introduced to interpolate the desired wrench and dominant cost weights, and an integrator alignment reset is applied at switching instants to keep the outer-loop proportional–integral–derivative (PID) output continuous. The allocator is further warm-started by projecting the previous solution onto the post-switch constraint box. The framework is integrated into the Mission-Oriented Operating Suite–Interval Programming (MOOS-IvP) autonomy middleware with adaptive line-of-sight (ALOS) guidance and adaptive PID motion control and is validated on the TS-100 AUV in water tank experiments. Comparative results against a PID-only baseline without control allocation and a variant without bumpless switching show reduced roll transients during the reverse-to-hover transition and improved hover-mode depth station keeping while maintaining feasible actuator commands under constraints. Full article
(This article belongs to the Section Ocean Engineering)
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16 pages, 2274 KB  
Article
Mine Ventilation Network Calibration Based on Slack Variables and Sequential Quadratic Programming
by Fengliang Wu, Ruitun Wang, Jun Cao and Jianan Gao
Processes 2026, 14(4), 715; https://doi.org/10.3390/pr14040715 - 21 Feb 2026
Viewed by 457
Abstract
In mine ventilation network calibration, sparse and inconsistent airflow measurements often lead to infeasibility in traditional optimization models. To overcome this challenge, this paper proposes a nonlinear programming calibration model incorporating slack variables. The model treats aerodynamic resistance corrections, airflow adjustments, unknown airflows, [...] Read more.
In mine ventilation network calibration, sparse and inconsistent airflow measurements often lead to infeasibility in traditional optimization models. To overcome this challenge, this paper proposes a nonlinear programming calibration model incorporating slack variables. The model treats aerodynamic resistance corrections, airflow adjustments, unknown airflows, and resistance lower-bound slack variables as decision variables. The objective function is formulated to minimize the weighted sum of squares of resistance corrections, while penalty terms account for airflow adjustments and slack variables. Constraints integrate Kirchhoff’s laws with relaxed inequality constraints for resistance lower bounds. A calibration tool integrated via the ObjectARX interface was developed using C++, utilizing the Sequential Quadratic Programming (SQP) algorithm for the solution. The method was validated via a case study of a network comprising 39 branches and 16 measured airflows, optimized under five distinct initial conditions. Results demonstrate that the inclusion of slack variables mathematically guarantees the existence of feasible solutions. With a resistance correction weight of 10−2 and a penalty coefficient of 105, the model applies only minimal necessary corrections to handle overly tight constraints or data conflicts. The SQP algorithm exhibits superior global convergence, consistently iterating to optimal solutions that satisfy network balance laws regardless of initial values. This approach effectively resolves the infeasibility and data conflict issues inherent in traditional methods, demonstrating significant robustness and practical engineering utility. Full article
(This article belongs to the Section Petroleum and Low-Carbon Energy Process Engineering)
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