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20 pages, 484 KB  
Article
Design of Extended Dissipative Approach via Memory Sampled-Data Control for Stabilization and Its Application to Mixed Traffic System
by Wimonnat Sukpol, Vadivel Rajarathinam, Porpattama Hammachukiattikul and Putsadee Pornphol
Mathematics 2025, 13(15), 2449; https://doi.org/10.3390/math13152449 - 29 Jul 2025
Viewed by 315
Abstract
This study examines the extended dissipativity analysis for newly designed mixed traffic systems (MTSs) utilizing the coupling memory sampled-data control (CMSDC) approach. The traffic flow creates a platoon, and the behavior of human-driven vehicles (HDVs) is presumed to adhere to the optimal velocity [...] Read more.
This study examines the extended dissipativity analysis for newly designed mixed traffic systems (MTSs) utilizing the coupling memory sampled-data control (CMSDC) approach. The traffic flow creates a platoon, and the behavior of human-driven vehicles (HDVs) is presumed to adhere to the optimal velocity model, with the acceleration of a single-linked automated vehicle regulated directly by a suggested CMSDC. The ultimate objective of this work is to present a CMSDC approach for optimizing traffic flow amidst disruptions. The primary emphasis is on the proper design of the CMSDC to ensure that the closed-loop MTS is extended dissipative and quadratically stable. A more generalized CMSDC methodology incorporating a time delay effect is created using a Bernoulli-distributed sequence. The existing Lyapunov–Krasovskii functional (LKF) and enhanced integral inequality methods offer sufficient conditions for the suggested system to achieve an extended dissipative performance index. The suggested criteria provide a comprehensive dissipative study, evaluating L2L, H, passivity, and dissipativity performance. A simulation example illustrates the accuracy and superiority of the proposed controller architecture for the MTS. Full article
(This article belongs to the Special Issue Modeling, Control, and Optimization for Transportation Systems)
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25 pages, 5508 KB  
Article
A Lightweight Network for Water Body Segmentation in Agricultural Remote Sensing Using Learnable Kalman Filters and Attention Mechanisms
by Dingyi Liao, Jun Sun, Zhiyong Deng, Yudong Zhao, Jiani Zhang and Dinghua Ou
Appl. Sci. 2025, 15(11), 6292; https://doi.org/10.3390/app15116292 - 3 Jun 2025
Cited by 1 | Viewed by 834
Abstract
Precise identification of water bodies in agricultural watersheds is crucial for irrigation, water resource management, and flood disaster prevention. However, the spectral noise caused by complex light and shadow interference and water quality differences, combined with the diverse shapes of water bodies and [...] Read more.
Precise identification of water bodies in agricultural watersheds is crucial for irrigation, water resource management, and flood disaster prevention. However, the spectral noise caused by complex light and shadow interference and water quality differences, combined with the diverse shapes of water bodies and the high computational cost of image processing, severely limits the accuracy of water body recognition in agricultural watersheds. This paper proposed a lightweight and efficient learnable Kalman filter and Deformable Convolutional Attention Network (LKF-DCANet). The encoder is built using a shallow Channel Attention-Enhanced Deformable Convolution module (CADCN), while the decoder combines a Convolutional Additive Token Mixer (CATM) and a learnable Kalman filter (LKF) to achieve adaptive noise suppression and enhance global context modeling. Additionally, a feature-based knowledge distillation strategy is employed to further improve the representational capacity of the lightweight model. Experimental results show that LKF-DCANet achieves an Intersection over Union (IoU) of 85.95% with only 0.22 M parameters on a public dataset. When transferred to a self-constructed UAV dataset, it achieves an IoU of 96.28%, demonstrating strong generalization ability. All experiments are conducted on RGB optical imagery, confirming that LKF-DCANet offers an efficient and highly versatile solution for water body segmentation in precision agriculture. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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18 pages, 352 KB  
Article
Novel Results on Global Asymptotic Stability of Time-Delayed Complex Valued Bidirectional Associative Memory Neural Networks
by N. Mohamed Thoiyab, Saravanan Shanmugam, Rajarathinam Vadivel and Nallappan Gunasekaran
Symmetry 2025, 17(6), 834; https://doi.org/10.3390/sym17060834 - 27 May 2025
Viewed by 327
Abstract
This study investigates the global asymptotic stability of hybrid bidirectional associative memory (BAM) complex-valued neural networks (CVNNs) with time-varying delays and uncertain parameters, where the system matrices are assumed to be symmetric. By constructing an appropriate Lyapunov–Krasovskii functional (LKF), new sufficient conditions are [...] Read more.
This study investigates the global asymptotic stability of hybrid bidirectional associative memory (BAM) complex-valued neural networks (CVNNs) with time-varying delays and uncertain parameters, where the system matrices are assumed to be symmetric. By constructing an appropriate Lyapunov–Krasovskii functional (LKF), new sufficient conditions are derived to guarantee the existence and uniqueness of equilibrium points, as well as to establish the global asymptotic stability of the proposed symmetric hybrid BAM CVNNs. The validity and effectiveness of the theoretical results are further demonstrated through detailed numerical examples. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Network Control)
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24 pages, 8162 KB  
Article
Fixed-Time Event-Triggered Control for High-Order Nonlinear Multi-Agent Systems Under Unknown Stochastic Time Delays
by Junyi Liu, Hongbo Han, Yuncong Ma and Maode Yan
Mathematics 2025, 13(10), 1639; https://doi.org/10.3390/math13101639 - 16 May 2025
Viewed by 712
Abstract
In this paper, the fixed-time control for high-order nonlinear multi-agent systems under unknown stochastic time delay is investigated via an event-triggered approach. First of all, RBF neural networks are utilized to approximate the system’s uncertain nonlinearities. After that, an event-triggered scheme, which is [...] Read more.
In this paper, the fixed-time control for high-order nonlinear multi-agent systems under unknown stochastic time delay is investigated via an event-triggered approach. First of all, RBF neural networks are utilized to approximate the system’s uncertain nonlinearities. After that, an event-triggered scheme, which is designed with a relative threshold for more flexible control, is proposed to alleviate the communication burden. In consideration of the unknown stochastic time delay in the inter-communication among high-order nonlinear multi-agent systems, the Lyapunov–Krasovskii functional (LKF) is used to construct the system’s Lyapunov function, specifically targeting the adverse effects caused by time delay. Further, the fixed-time stability theory is employed to ensure that the convergence time remains independent of the initial values. Finally, the proposed control strategy is validated through numerical simulations. Full article
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14 pages, 269 KB  
Article
Joint Angular Kinematics and Gross Motor Function in Typically Developing Healthy Children
by Monday Omoniyi Moses, Ngozi Florence Onuegbu, Prince De-Gualle Deku, Mary Abena Nyarko, Lydia Boampong Owusu, Abigael Omowumi Emikpe, Emmanuel Babatunde John, Rahul Soangra, Abiboye Cheduko Yifieyeh and Nicholas Akinwale Titiloye
Children 2025, 12(3), 280; https://doi.org/10.3390/children12030280 - 25 Feb 2025
Viewed by 899
Abstract
Objective: The aim of this study was to establish the interactions between joint angular kinematics and gross motor function in typically developing healthy Ghanaian children. Methods: A descriptive cross-sectional study design was employed. A total of 150 (69 (46.0%), 3.25 ± 0.08-year-old boys [...] Read more.
Objective: The aim of this study was to establish the interactions between joint angular kinematics and gross motor function in typically developing healthy Ghanaian children. Methods: A descriptive cross-sectional study design was employed. A total of 150 (69 (46.0%), 3.25 ± 0.08-year-old boys and 81 (54.0%), 3.25 ± 0.06-year-old girls) 2–4-year-old children were recruited. Joint angular kinematic variables [left hip flexion (LHF), left hip extension (LHE), right hip flexion (RHF), left knee flexion (LKF), right hip extension (RHE), left knee extension (LKE), right knee flexion (RKF), left ankle dorsi-flexion (LADF), right knee extension (RKE), right ankle plantar flexion (RAPF), left ankle plantar flexion (LAPF), and right ankle dorsi-flexion (RADF)] and gross motor function (lying and rolling, sitting, crawling and kneeling, standing, and walking, running, and jumping) were measured with standard scales. Results: The correlations between lying and rolling vs. RHE (r = 0.221; p-value < 0.01), LKE (r = −0.267; p-value < 0.01), LAPF (r = 0.264; p-value < 0.01), and RADF (r = 0.240; p-value < 0.01); crawling and kneeling vs. LKE (r = 0.196; p-value < 0.05) and RADF (r = 0.188; p-value < 0.05); and walking, running, and jumping vs. LKE (r = −0.214; p-value < 0.01) and RADF (r = −0.207; p-value < 0.05) were significant. Conclusions: There was a negative correlation between joint angular kinematics and total gross motor function in this sampled population. Typically, developing healthy children should be exposed to a range of motion, flexibility, and active transportation programs for optimal active lifestyles and improvements in gross motor skills. Full article
(This article belongs to the Section Pediatric Neurology & Neurodevelopmental Disorders)
31 pages, 7203 KB  
Article
An Electro-Magnetic Log (EML) Integrated Navigation Algorithm Based on Hidden Markov Model (HMM) and Cross-Noise Linear Kalman Filter
by Haosu Zhang, Liang Yang, Lei Zhang, Yong Du, Chaoqi Chen, Wei Mu and Lingji Xu
Sensors 2025, 25(4), 1015; https://doi.org/10.3390/s25041015 - 8 Feb 2025
Viewed by 1096
Abstract
In this paper, an EML (electro-magnetic log) integrated navigation algorithm based on the HMM (hidden Markov model) and CNLKF (cross-noise linear Kalman filter) is proposed, which is suitable for SINS (strapdown inertial navigation system)/EML/GNSS (global navigation satellite system) integrated navigation systems for small [...] Read more.
In this paper, an EML (electro-magnetic log) integrated navigation algorithm based on the HMM (hidden Markov model) and CNLKF (cross-noise linear Kalman filter) is proposed, which is suitable for SINS (strapdown inertial navigation system)/EML/GNSS (global navigation satellite system) integrated navigation systems for small or medium-sized AUV (autonomous underwater vehicle). The algorithm employs the following five techniques: ① the HMM-based pre-processing algorithm of EML data; ② the CNLKF-based fusion algorithm of SINS/EML information; ③ the MALKF (modified adaptive linear Kalman filter)-based algorithm of GNSS-based calibration; ④ the estimation algorithm of the current speed based on output from MALKF and GNSS; ⑤ the feedback correction of LKF (linear Kalman filter). The principle analysis of the algorithm, the modeling process, and the flow chart of the algorithm are given in this paper. The sea trial of a small-sized AUV shows that the endpoint positioning error of the proposed/traditional algorithm by this paper is 20.5 m/712.1 m. The speed of the water current could be relatively accurately estimated by the proposed algorithm. Therefore, the algorithm has the advantages of high accuracy, strong anti-interference ability (it can effectively shield the outliers of EML and GNSS), strong adaptability to complex environments, and high engineering practicality. In addition, compared with the traditional DVL (Doppler velocity log), EML has the advantages of great concealment, low cost, light weight, small size, and low power consumption. Full article
(This article belongs to the Section Navigation and Positioning)
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36 pages, 9454 KB  
Article
Integrated Navigation Algorithm for Autonomous Underwater Vehicle Based on Linear Kalman Filter, Thrust Model, and Propeller Tachometer
by Haosu Zhang, Yueying Cai, Jin Yue, Wei Mu, Shiyin Zhou, Defei Jin and Lingji Xu
J. Mar. Sci. Eng. 2025, 13(2), 303; https://doi.org/10.3390/jmse13020303 - 6 Feb 2025
Viewed by 1221
Abstract
For the purpose of reducing the cost, size, and weight of the integrated navigation system of an AUV (autonomous underwater vehicle), and improving the stealth of this system, an integrated navigation algorithm based on a propeller tachometer is proposed. The algorithm consists of [...] Read more.
For the purpose of reducing the cost, size, and weight of the integrated navigation system of an AUV (autonomous underwater vehicle), and improving the stealth of this system, an integrated navigation algorithm based on a propeller tachometer is proposed. The algorithm consists of five steps: ① establishing the resistance model of AUV, ② establishing the thrust model, ③ utilizing the measured speeds obtained from the AUV’s voyage trials for calibration, ④ discrimination and replacement of outliers from the tachometer measurements, and ⑤ establishing a linear Kalman filter (LKF) with water currents as state variables. This paper provides the modeling procedure, formula derivations, model parameters, and algorithm process, etc. Through research and analysis, the proposed algorithm’s accuracy has been improved. The specific values of the localization error are detailed in the main text. Therefore, the proposed algorithm has high accuracy, a strong anti-interference capability, and good robustness. Moreover, it exhibits certain adaptability to complex environments and value for practical engineering. Full article
(This article belongs to the Section Ocean Engineering)
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17 pages, 5755 KB  
Article
A Hybrid Architecture for Safe Human–Robot Industrial Tasks
by Gaetano Lettera, Daniele Costa and Massimo Callegari
Appl. Sci. 2025, 15(3), 1158; https://doi.org/10.3390/app15031158 - 24 Jan 2025
Cited by 2 | Viewed by 1679
Abstract
In the context of Industry 5.0, human–robot collaboration (HRC) is increasingly crucial for enabling safe and efficient operations in shared industrial workspaces. This study aims to implement a hybrid robotic architecture based on the Speed and Separation Monitoring (SSM) collaborative scenario defined in [...] Read more.
In the context of Industry 5.0, human–robot collaboration (HRC) is increasingly crucial for enabling safe and efficient operations in shared industrial workspaces. This study aims to implement a hybrid robotic architecture based on the Speed and Separation Monitoring (SSM) collaborative scenario defined in ISO/TS 15066. The system calculates the minimum protective separation distance between the robot and the operators and slows down or stops the robot according to the risk assessment computed in real time. Compared to existing solutions, the approach prevents collisions and maximizes workcell production by reducing the robot speed only when the calculated safety index indicates an imminent risk of collision. The proposed distributed software architecture utilizes the ROS2 framework, integrating three modules: (1) a fast and reliable human tracking module based on the OptiTrack system that considerably reduces latency times or false positives, (2) an intention estimation (IE) module, employing a linear Kalman filter (LKF) to predict the operator’s next position and velocity, thus considering the current scenario and not the worst case, and (3) a robot control module that computes the protective separation distance and assesses the safety index by measuring the Euclidean distance between operators and the robot. This module dynamically adjusts robot speed to maintain safety while minimizing unnecessary slowdowns, ensuring the efficiency of collaborative tasks. Experimental results demonstrate that the proposed system effectively balances safety and speed, optimizing overall performance in human–robot collaborative industrial environments, with significant improvements in productivity and reduced risk of accidents. Full article
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15 pages, 403 KB  
Article
Guaranteed Cost Control of Singular Fuzzy Time-Delay Systems Based on Proportional Plus Derivative Feedback
by Huayang Zhang, Hebin Wang and Xin Wang
Electronics 2024, 13(22), 4554; https://doi.org/10.3390/electronics13224554 - 20 Nov 2024
Cited by 1 | Viewed by 872
Abstract
This paper explores the guaranteed cost control issue for singular Takagi-Sugeno (T-S) fuzzy systems with time delay. An augmented Lyapunov-Krasovskii functional (LKF) is adopted to analyze the system’s stabilization, and sufficient conditions are established based on Lyapunov stability theory. The method of free [...] Read more.
This paper explores the guaranteed cost control issue for singular Takagi-Sugeno (T-S) fuzzy systems with time delay. An augmented Lyapunov-Krasovskii functional (LKF) is adopted to analyze the system’s stabilization, and sufficient conditions are established based on Lyapunov stability theory. The method of free weight matrices is employed to provide a systematic approach for determining the controller parameters. Additionally, two compelling examples are presented to demonstrate the viability of the proposed methods. Full article
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24 pages, 5276 KB  
Article
An Improved LKF Integrated Navigation Algorithm Without GNSS Signal for Vehicles with Fixed-Motion Trajectory
by Haosu Zhang, Zihao Wang, Shiyin Zhou, Zhiying Wei, Jianming Miao, Lingji Xu and Tao Liu
Electronics 2024, 13(22), 4498; https://doi.org/10.3390/electronics13224498 - 15 Nov 2024
Viewed by 2324
Abstract
Without a GNSS (global navigation satellite system) signal, the integrated navigation system in vehicles with a fixed trajectory (e.g., railcars) is limited to the use of micro-electromechanical system-inertial navigation system (MEMS-INS) and odometer (ODO). Due to the significant measurement error of the MEMS [...] Read more.
Without a GNSS (global navigation satellite system) signal, the integrated navigation system in vehicles with a fixed trajectory (e.g., railcars) is limited to the use of micro-electromechanical system-inertial navigation system (MEMS-INS) and odometer (ODO). Due to the significant measurement error of the MEMS inertial device and the inability of ODO to output attitude, the positioning error is generally large. To address this problem, this paper presents a new integrated navigation algorithm based on a dynamically constrained Kalman model. By analyzing the dynamics of a railcar, several new observations have been investigated, including errors of up and lateral velocity, centripetal acceleration, centripetal D-value (difference value), and an up-gyro bias. The state transition matrix and observation matrix for the error state model are represented. To improve navigation accuracy, virtual noise technology is applied to correct errors of up and lateral velocity. The vehicle-running experiment conducted within 240 s demonstrates that the positioning error rate of the dead-reckoning method based on MEMS-INS is 83.5%, whereas the proposed method exhibits a rate of 4.9%. Therefore, the accuracy of positioning can be significantly enhanced. Full article
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19 pages, 972 KB  
Article
Robust H Control for Autonomous Underwater Vehicle’s Time-Varying Delay Systems under Unknown Random Parameter Uncertainties and Cyber-Attacks
by Soundararajan Vimal Kumar and Jonghoek Kim
Appl. Sci. 2024, 14(19), 8827; https://doi.org/10.3390/app14198827 - 1 Oct 2024
Cited by 4 | Viewed by 1008
Abstract
This paper investigates robust H-based control for autonomous underwater vehicle (AUV) systems under time-varying delay, model uncertainties, and cyber-attacks. Sensor and actuator cyber-attacks can cause faults in the overall AUV system. In addition, the behavior of the system can be affected [...] Read more.
This paper investigates robust H-based control for autonomous underwater vehicle (AUV) systems under time-varying delay, model uncertainties, and cyber-attacks. Sensor and actuator cyber-attacks can cause faults in the overall AUV system. In addition, the behavior of the system can be affected by the presence of complexities, such as unknown random uncertainties that occur in system modeling. In this paper, the robustness against unpredictable random uncertainties is investigated by considering unknown but norm-bounded (UBB) random uncertainties. By constructing a proper Lyapunov–Krasovskii functional (LKF) and using linear matrix inequality (LMI) techniques, new stability criteria in the form of LMIs are derived such that the AUV system is stable. Moreover, this work is novel in addressing robust H control, which considers time-varying delay, cyber-attacks, and randomly occurring uncertainties for AUV systems. Finally, the effectiveness of the proposed results is demonstrated through two examples and their computer simulations. Full article
(This article belongs to the Section Robotics and Automation)
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33 pages, 1560 KB  
Article
New Event-Triggered Synchronization Criteria for Fractional-Order Complex-Valued Neural Networks with Additive Time-Varying Delays
by Haiyang Zhang, Yi Zhao, Lianglin Xiong, Junzhou Dai and Yi Zhang
Fractal Fract. 2024, 8(10), 569; https://doi.org/10.3390/fractalfract8100569 - 28 Sep 2024
Viewed by 1110
Abstract
This paper explores the synchronization control issue for a class of fractional-order Complex-valued Neural Networks (FOCVNNs) with additive time-varying delays (TVDs) utilizing a sampled-data-based event-triggered mechanism (SDBETM). First, an innovative free-matrix-based fractional-order integral inequality (FMBFOII) and an improved fractional-order complex-valued integral inequality (FOCVII) [...] Read more.
This paper explores the synchronization control issue for a class of fractional-order Complex-valued Neural Networks (FOCVNNs) with additive time-varying delays (TVDs) utilizing a sampled-data-based event-triggered mechanism (SDBETM). First, an innovative free-matrix-based fractional-order integral inequality (FMBFOII) and an improved fractional-order complex-valued integral inequality (FOCVII) are proposed, which are less conservative than the existing classical fractional-order integral inequality (FOII). Secondly, an SDBETM is inducted to conserve network resources. In addition, a novel Lyapunov–Krasovskii functional (LKF) enriched with additional information regarding the fractional-order derivative, additive TVDs, and triggering instants is constructed. Then, through the integration of the innovative FOCVII, LKF, SDBETM, and other analytical methodologies, we deduce two criteria in the form of linear matrix inequalities (LMIs) to ensure the synchronization of the master–slave FOCVNNs. Finally, numerical simulations are illustrated to confirm the validity of the proposed results. Full article
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20 pages, 1623 KB  
Article
Adaptive Finite-Time-Based Neural Optimal Control of Time-Delayed Wheeled Mobile Robotics Systems
by Shu Li, Tao Ren, Liang Ding and Lei Liu
Sensors 2024, 24(17), 5462; https://doi.org/10.3390/s24175462 - 23 Aug 2024
Viewed by 1864
Abstract
For nonlinear systems with uncertain state time delays, an adaptive neural optimal tracking control method based on finite time is designed. With the help of the appropriate LKFs, the time-delay problem is handled. A novel nonquadratic Hamilton–Jacobi–Bellman (HJB) function is defined, where finite [...] Read more.
For nonlinear systems with uncertain state time delays, an adaptive neural optimal tracking control method based on finite time is designed. With the help of the appropriate LKFs, the time-delay problem is handled. A novel nonquadratic Hamilton–Jacobi–Bellman (HJB) function is defined, where finite time is selected as the upper limit of integration. This function contains information on the state time delay, while also maintaining the basic information. To meet specific requirements, the integral reinforcement learning method is employed to solve the ideal HJB function. Then, a tracking controller is designed to ensure finite-time convergence and optimization of the controlled system. This involves the evaluation and execution of gradient descent updates of neural network weights based on a reinforcement learning architecture. The semi-global practical finite-time stability of the controlled system and the finite-time convergence of the tracking error are guaranteed. Full article
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19 pages, 507 KB  
Article
Enhancing Stability Criteria for Linear Systems with Interval Time-Varying Delays via an Augmented Lyapunov–Krasovskii Functional
by Dong-Hoon Lee, Yeong-Jae Kim, Seung-Hoon Lee and Oh-Min Kwon
Mathematics 2024, 12(14), 2241; https://doi.org/10.3390/math12142241 - 18 Jul 2024
Cited by 3 | Viewed by 1094
Abstract
This work investigates the stability conditions for linear systems with time-varying delays via an augmented Lyapunov–Krasovskii functional (LKF). Two types of augmented LKFs with cross terms in integrals are suggested to improve the stability conditions for interval time-varying linear systems. In this work, [...] Read more.
This work investigates the stability conditions for linear systems with time-varying delays via an augmented Lyapunov–Krasovskii functional (LKF). Two types of augmented LKFs with cross terms in integrals are suggested to improve the stability conditions for interval time-varying linear systems. In this work, the compositions of the LKFs are considered to enhance the feasible region of the stability criterion for linear systems. Mathematical tools such as Wirtinger-based integral inequality (WBII), zero equalities, reciprocally convex approach, and Finsler’s lemma are utilized to solve the problem of stability criteria. Two sufficient conditions are derived to guarantee the asymptotic stability of the systems using linear matrix inequality (LMI). First, asymptotic stability criteria are induced by constructing the new augmented LKFs in Theorem 1. Then, simplified LKFs in Corollary 1 are proposed to show the effectiveness of Theorem 1. Second, asymmetric LKFs are shown to reduce the conservatism and the number of decision variables in Theorem 2. Finally, the advantages of the proposed criteria are verified by comparing maximum delay bounds in four examples. Four numerical examples show that the proposed Theorems 1 and 2 obtain less conservative results than existing outcomes. Particularly, Example 2 shows that the asymmetric LKF methods of Theorem 2 can provide larger delay bounds and fewer decision variables than Theorem 1 in some specific systems. Full article
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24 pages, 4888 KB  
Article
Compound Control Design of Near-Space Hypersonic Vehicle Based on a Time-Varying Linear Quadratic Regulator and Sliding Mode Method
by Huan Wang, Di Zhou, Yiqun Zhang and Chaofei Lou
Aerospace 2024, 11(7), 567; https://doi.org/10.3390/aerospace11070567 - 10 Jul 2024
Cited by 3 | Viewed by 1342
Abstract
The design of a hypersonic vehicle controller has been an active research field in the last decade, especially when the vehicle is studied as a time-varying system. A time-varying compound control method is proposed for a hypersonic vehicle controlled by the direct lateral [...] Read more.
The design of a hypersonic vehicle controller has been an active research field in the last decade, especially when the vehicle is studied as a time-varying system. A time-varying compound control method is proposed for a hypersonic vehicle controlled by the direct lateral force and the aerodynamic force. The compound control method consists of a time-varying linear quadratic regulator (LQR) control law for the aerodynamic rudder and a sliding mode control law for the lateral thrusters. When the air rudder cannot continuously produce control force and torque, the direct lateral force is added to the system. To solve the problem that LQR cannot directly obtain the analytical solution of the time-varying system, a novel approach to approximate analytical solutions using Jacobi polynomials is proposed in this paper. Finally, the stability of the time-varying compound control system is proven by the Lyapunov–Krasovskii functional (LKF). The simulation results show that the proposed compound control method is effective and can improve the fast response ability of the system. Full article
(This article belongs to the Special Issue Challenges and Innovations in Aircraft Flight Control)
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