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Keywords = RBFNN-based adaptive updating

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19 pages, 1059 KB  
Article
Adaptive Sliding Mode Control Incorporating Improved Integral Compensation Mechanism for Vehicle Platoon with Input Delays
by Yunpeng Ding, Yiguang Wang and Xiaojie Li
Sensors 2026, 26(2), 615; https://doi.org/10.3390/s26020615 - 16 Jan 2026
Abstract
This study focuses on investigating the adaptive sliding mode control (SMC) problem for connected vehicles with input delays and unknown time-varying control coefficients. As a result of wear and tear of mechanical components, throttle response lags, and the internal data processing time of [...] Read more.
This study focuses on investigating the adaptive sliding mode control (SMC) problem for connected vehicles with input delays and unknown time-varying control coefficients. As a result of wear and tear of mechanical components, throttle response lags, and the internal data processing time of the controller, input delays widely exist in vehicle actuators. Since input delays may lead to instability of the vehicle platoon, an improved integral compensation mechanism (ICM) with the adjustment factor for input delays is developed to improve the platoon’s robustness. As the actuator efficiency, drive mechanism, and load of the vehicle may change during operation, the control coefficients of vehicle dynamics are usually unknown and time-varying. A novel adaptive updating mechanism utilizing a radial basis function neural network (RBFNN) is designed to deal with the unknown time-varying control coefficients, thereby improving the vehicle platoon’s tracking performance. By integrating the improved ICM and the RBFNN-based adaptive updating mechanism (RBFNN−AUM), an innovative distributed adaptive control scheme using sliding mode techniques is proposed to guarantee that the convergence of state errors to a predefined region and accomplish the vehicle platoon’s control objectives. Comparative numerical results confirm the effectiveness and superiority of the developed control strategy over existing method. Full article
(This article belongs to the Section Vehicular Sensing)
23 pages, 2646 KB  
Article
Model-Reconstructed RBFNN-DOB for FJR Trajectory Control with External Disturbances
by Tianmeng Li, Caiwen Ma, Yanbing Liang, Fan Wang and Zhou Ji
Sensors 2025, 25(18), 5608; https://doi.org/10.3390/s25185608 - 9 Sep 2025
Viewed by 1036
Abstract
Parameter uncertainties and fluctuating disturbances have posed significant challenges to the smooth and precise control of Flexible Joint Robots (FJRs) in industrial environments. To mitigate such disturbances, Disturbance Observers (DOBs) are commonly employed; however, the model uncertainties inherent in FJR systems make accurate [...] Read more.
Parameter uncertainties and fluctuating disturbances have posed significant challenges to the smooth and precise control of Flexible Joint Robots (FJRs) in industrial environments. To mitigate such disturbances, Disturbance Observers (DOBs) are commonly employed; however, the model uncertainties inherent in FJR systems make accurate dynamic modeling challenging, and the efficacy of DOBs hinges heavily on the accuracy of the dynamic model, which limits their applicability to FJR control. This paper presents a hybrid RBFNN-based Disturbance Observer (RBFNNDOB) state feedback controller for FJRs. By combining a nominal model-based DOB with an RBFNN, this method effectively addresses the unknown dynamics of FJRs while simultaneously compensating for external time-varying disturbances. In this framework, an adaptive neural network weight update law is formulated using Lyapunov stability theory. This enables the RBFNN to selectively estimate the unmodeled uncertainties in FJR dynamics, thereby minimizing computational redundancy in model estimation while allowing dynamic compensation for residual uncertainties beyond the nominal model and DOB estimation errors—ultimately enhancing computational efficiency and achieving robust compensation for rapidly changing disturbances. The boundedness of the tracking error is proven using the Lyapunov approach, and experimental validation is conducted on the FJR system to confirm the efficacy of the proposed control method. Full article
(This article belongs to the Section Sensors and Robotics)
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25 pages, 2473 KB  
Article
Predefined-Time Adaptive Neural Control with Event-Triggering for Robust Trajectory Tracking of Underactuated Marine Vessels
by Hui An, Zhanyang Yu, Jianhua Zhang, Xinxin Wang and Cheng Siong Chin
Processes 2025, 13(8), 2443; https://doi.org/10.3390/pr13082443 - 1 Aug 2025
Viewed by 699
Abstract
This paper addresses the trajectory tracking control problem of underactuated ships in ocean engineering, which faces the dual challenges of tracking error time–performance regulation and robustness design due to the system’s underactuated characteristics, model uncertainties, and external disturbances. Aiming to address the issues [...] Read more.
This paper addresses the trajectory tracking control problem of underactuated ships in ocean engineering, which faces the dual challenges of tracking error time–performance regulation and robustness design due to the system’s underactuated characteristics, model uncertainties, and external disturbances. Aiming to address the issues of traditional finite-time control (convergence time dependent on initial states) and fixed-time control (control chattering and parameter conservativeness), this paper proposes a predefined-time adaptive control framework that integrates an event-triggered mechanism and neural networks. By constructing a Lyapunov function with time-varying weights and designing non-periodic dynamically updated dual triggering conditions, the convergence process of tracking errors is strictly constrained within a user-prespecified time window without relying on initial states or introducing non-smooth terms. An adaptive approximator based on radial basis function neural networks (RBF-NNs) is employed to compensate for unknown nonlinear dynamics and external disturbances in real-time. Combined with the event-triggered mechanism, it dynamically adjusts the update instances of control inputs, ensuring prespecified tracking accuracy while significantly reducing computational resource consumption. Theoretical analysis shows that all signals in the closed-loop system are uniformly ultimately bounded, tracking errors converge to a neighborhood of the origin within the predefined-time, and the update frequency of control inputs exhibits a linear relationship with the predefined-time, avoiding Zeno behavior. Simulation results verify the effectiveness of the proposed method in complex marine environments. Compared with traditional control strategies, it achieves more accurate trajectory tracking, faster response, and a substantial reduction in control input update frequency, providing an efficient solution for the engineering implementation of embedded control systems in unmanned ships. Full article
(This article belongs to the Special Issue Design and Analysis of Adaptive Identification and Control)
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20 pages, 3825 KB  
Article
Nonlinear Observer-Based Distributed Adaptive Fault-Tolerant Control for Vehicle Platoon with Actuator Faults, Saturation, and External Disturbances
by Anqing Tong, Yiguang Wang, Xiaojie Li, Xiaoyan Zhan, Minghao Yang and Yunpeng Ding
Electronics 2025, 14(14), 2879; https://doi.org/10.3390/electronics14142879 - 18 Jul 2025
Viewed by 660
Abstract
This work studies the issue of distributed fault-tolerant control for a vehicle platoon with actuator faults, saturation, and external disturbances. As the degrees of wear, age, and overcurrent of a vehicle actuator might change during the working process, it is more practical to [...] Read more.
This work studies the issue of distributed fault-tolerant control for a vehicle platoon with actuator faults, saturation, and external disturbances. As the degrees of wear, age, and overcurrent of a vehicle actuator might change during the working process, it is more practical to consider the actuator faults to be time-varying rather than constant. Considering a situation in which actuator faults may cause partial actuator effectiveness loss, a novel adaptive updating mechanism is developed to estimate this loss. A new nonlinear observer is proposed to estimate external disturbances without requiring us to know their upper bounds. Since non-zero initial spacing errors (ISEs) may cause instability of the vehicle platoon, a novel exponential spacing policy (ESP) is devised to mitigate the adverse effects of non-zero ISEs. Based on the developed nonlinear observer, adaptive updating mechanism, radial basis function neural network (RBFNN), and the ESP, a novel nonlinear observer-based distributed adaptive fault-tolerant control strategy is proposed to achieve the objectives of platoon control. Lyapunov theory is utilized to prove the vehicle platoon’s stability. The rightness and effectiveness of the developed control strategy are validated using a numerical example. Full article
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28 pages, 11429 KB  
Article
Trajectory Tracking of Unmanned Surface Vessels Based on Robust Neural Networks and Adaptive Control
by Ziming Wang, Chunliang Qiu, Zaopeng Dong, Shaobo Cheng, Long Zheng and Shunhuai Chen
J. Mar. Sci. Eng. 2025, 13(7), 1341; https://doi.org/10.3390/jmse13071341 - 13 Jul 2025
Cited by 2 | Viewed by 902
Abstract
In this paper, a robust neural adaptive controller is proposed for the trajectory tracking control problem of unmanned surface vessels (USVs), considering model uncertainty, time-varying environmental disturbance, and actuator saturation. First, measurement errors in acceleration signals are eliminated through filtering techniques and a [...] Read more.
In this paper, a robust neural adaptive controller is proposed for the trajectory tracking control problem of unmanned surface vessels (USVs), considering model uncertainty, time-varying environmental disturbance, and actuator saturation. First, measurement errors in acceleration signals are eliminated through filtering techniques and a series of auxiliary variables, and after linearly parameterizing the USV dynamic model, a parameter adaptive update law is developed based on Lyapunov’s second method to estimate unknown dynamic parameters in the USV dynamics model. This parameter adaptive update law enables online identification of all USV dynamic parameters during trajectory tracking while ensuring convergence of the estimation errors. Second, a radial basis function neural network (RBF-NN) is employed to approximate unmodeled dynamics in the USV system, and on this basis, a robust damping term is designed based on neural damping technology to compensate for environmental disturbances and unmodeled dynamics. Subsequently, a trajectory tracking controller with parameter adaptation law and robust damping term is proposed using Lyapunov theory and adaptive control techniques. In addition, finite-time auxiliary variables are also added to the controller to handle the actuator saturation problem. Signal delay compensators are designed to compensate for input signal delays in the control system, thereby enhancing controller reliability. The proposed controller ensures robustness in trajectory tracking under model uncertainties and time-varying environmental disturbances. Finally, the convergence of each signal of the closed-loop system is proved based on Lyapunov theory. And the effectiveness of the control system is verified by numerical simulation experiments. Full article
(This article belongs to the Section Ocean Engineering)
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22 pages, 7052 KB  
Article
Data-Driven Dynamic Security Partition Assessment of Power Systems Based on Symmetric Electrical Distance Matrix and Chebyshev Distance
by Hang Qi, Ruiyang Su, Runjia Sun and Jiongcheng Yan
Symmetry 2024, 16(10), 1355; https://doi.org/10.3390/sym16101355 - 12 Oct 2024
Cited by 1 | Viewed by 2147
Abstract
A rapid dynamic security assessment (DSA) is crucial for online preventive and restoration decision-making. The deep learning-based DSA models have high efficiency and accuracy. However, the complex model structure and high training cost make them hard to update quickly. This paper proposes a [...] Read more.
A rapid dynamic security assessment (DSA) is crucial for online preventive and restoration decision-making. The deep learning-based DSA models have high efficiency and accuracy. However, the complex model structure and high training cost make them hard to update quickly. This paper proposes a dynamic security partition assessment method, aiming to develop accurate and incrementally updated DSA models with simple structures. Firstly, the power grid is self-adaptively partitioned into several local regions based on the mean shift algorithm. The input of the mean shift algorithm is a symmetric electrical distance matrix, and the distance metric is the Chebyshev distance. Secondly, high-level features of operating conditions are extracted based on the stacked denoising autoencoder. The symmetric electrical distance matrix is modified to represent fault locations in local regions. Finally, DSA models are constructed for fault locations in each region based on the radial basis function neural network (RBFNN) and Chebyshev distance. An online incremental updating strategy is designed to enhance the model adaptability. With the simulation software PSS/E 33.4.0, the proposed dynamic security partition assessment method is verified in a simplified provincial system and a large-scale practical system in China. Test results demonstrate that the Chebyshev distance can improve the partition quality of the mean shift algorithm by approximately 50%. The RBFNN-based partition assessment model achieves an accuracy of 98.96%, which is higher than the unified assessment with complex models. The proposed incremental updating strategy achieves an accuracy of over 98% and shortens the updating time to 30 s, which can meet the efficiency of online application. Full article
(This article belongs to the Special Issue New Power System and Symmetry)
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18 pages, 413 KB  
Article
Near-Optimal Tracking Control of Partially Unknown Discrete-Time Nonlinear Systems Based on Radial Basis Function Neural Network
by Jiashun Huang, Dengguo Xu, Yahui Li and Yan Ma
Mathematics 2024, 12(8), 1146; https://doi.org/10.3390/math12081146 - 10 Apr 2024
Cited by 7 | Viewed by 1514
Abstract
This paper proposes an optimal tracking control scheme through adaptive dynamic programming (ADP) for a class of partially unknown discrete-time (DT) nonlinear systems based on a radial basis function neural network (RBF-NN). In order to acquire the unknown system dynamics, we use two [...] Read more.
This paper proposes an optimal tracking control scheme through adaptive dynamic programming (ADP) for a class of partially unknown discrete-time (DT) nonlinear systems based on a radial basis function neural network (RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs; the first one is used to construct the identifier, and the other one is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. The optimal feedback control and the cost function are derived via feedforward neural network approximation, and a means of regulating the tracking error is proposed. The critic network and the actor network were trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation within the ADP framework. Simulations were carried out to verify the effectiveness of the optimal tracking control technique using the neural networks. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Control)
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18 pages, 8241 KB  
Article
Adaptive Neural Consensus of Unknown Non-Linear Multi-Agent Systems with Communication Noises under Markov Switching Topologies
by Shaoyan Guo and Longhan Xie
Mathematics 2024, 12(1), 133; https://doi.org/10.3390/math12010133 - 31 Dec 2023
Cited by 4 | Viewed by 2126
Abstract
In this paper, the adaptive consensus problem of unknown non-linear multi-agent systems (MAs) with communication noises under Markov switching topologies is studied. Based on the adaptive control theory, a novel distributed control protocol for non-linear multi-agent systems is designed. It consists of the [...] Read more.
In this paper, the adaptive consensus problem of unknown non-linear multi-agent systems (MAs) with communication noises under Markov switching topologies is studied. Based on the adaptive control theory, a novel distributed control protocol for non-linear multi-agent systems is designed. It consists of the local interfered relative information and the estimation of the unknown dynamic. The Radial Basis Function networks (RBFNNs) approximate the nonlinear dynamic, and the estimated weight matrix is updated by utilizing the measurable state information. Then, using the stochastic Lyapunov analysis method, conditions for attaining consensus are derived on the consensus gain and the weight of RBFNNs. The main findings of this paper are as follows: the consensus control of multi-agent systems under more complicated and practical circumstances, including unknown nonlinear dynamic, Markov switching topologies and communication noises, is discussed; the nonlinear dynamic is approximated based on the RBFNNs and the local interfered relative information; the consensus gain k must to be small to guarantee the consensus performance; and the proposed algorithm is validated by the numerical simulations finally. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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33 pages, 8340 KB  
Article
The Enhanced Wagner–Hagras OLS–BP Hybrid Algorithm for Training IT3 NSFLS-1 for Temperature Prediction in HSM Processes
by Gerardo Maximiliano Méndez, Ismael López-Juárez, María Aracelia Alcorta García, Dulce Citlalli Martinez-Peon and Pascual Noradino Montes-Dorantes
Mathematics 2023, 11(24), 4933; https://doi.org/10.3390/math11244933 - 12 Dec 2023
Cited by 3 | Viewed by 2285
Abstract
This paper presents (a) a novel hybrid learning method to train interval type-1 non-singleton type-3 fuzzy logic systems (IT3 NSFLS-1), (b) a novel method, named enhanced Wagner–Hagras (EWH) applied to IT3 NSFLS-1 fuzzy systems, which includes the level alpha 0 output to calculate [...] Read more.
This paper presents (a) a novel hybrid learning method to train interval type-1 non-singleton type-3 fuzzy logic systems (IT3 NSFLS-1), (b) a novel method, named enhanced Wagner–Hagras (EWH) applied to IT3 NSFLS-1 fuzzy systems, which includes the level alpha 0 output to calculate the output y alpha using the average of the outputs y alpha k instead of their weighted average, and (c) the novel application of the proposed methodology to solve the problem of transfer bar surface temperature prediction in a hot strip mill. The development of the proposed methodology uses the orthogonal least square (OLS) method to train the consequent parameters and the backpropagation (BP) method to train the antecedent parameters. This methodology dynamically changes the parameters of only the level alpha 0, minimizing some criterion functions as new information becomes available to each level alpha k. The precursor sets are type-2 fuzzy sets, the consequent sets are fuzzy centroids, the inputs are type-1 non-singleton fuzzy numbers with uncertain standard deviations, and the secondary membership functions are modeled as two Gaussians with uncertain standard deviation and the same mean. Based on the firing set of the level alpha 0, the proposed methodology calculates each firing set of each level alpha k to dynamically construct and update the proposed EWH IT3 NSFLS-1 (OLS–BP) system. The proposed enhanced fuzzy system and the proposed hybrid learning algorithm were applied in a hot strip mill facility to predict the transfer bar surface temperature at the finishing mill entry zone using, as inputs, (1) the surface temperature measured by the pyrometer located at the roughing mill exit and (2) the time taken to translate the transfer bar from the exit of the roughing mill to the entry of the descale breaker of the finishing mill. Several fuzzy tools were used to make the benchmarking compositions: type-1 singleton fuzzy logic systems (T1 SFLS), type-1 adaptive network fuzzy inference systems (T1 ANFIS), type-1 radial basis function neural networks (T1 RBFNN), interval singleton type-2 fuzzy logic systems (IT2 SFLS), interval type-1 non-singleton type-2 fuzzy logic systems (IT2 NSFLS-1), type-2 ANFIS (IT2 ANFIS), IT2 RBFNN, general singleton type-2 fuzzy logic systems (GT2 SFLS), general type-1 non-singleton type-2 fuzzy logic systems (GT2 NSFLS-1), interval singleton type-3 fuzzy logic systems (IT3 SFLS), and interval type-1 non-singleton type-3 fuzzy systems (IT3 NSFLS-1). The experiments show that the proposed EWH IT3 NSFLS-1 (OLS–BP) system presented superior capability to learn the knowledge and to predict the surface temperature with the lower prediction error. Full article
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19 pages, 575 KB  
Article
Hybrid Backstepping Control of a Quadrotor Using a Radial Basis Function Neural Network
by Muhammad Maaruf, Waleed M. Hamanah and Mohammad A. Abido
Mathematics 2023, 11(4), 991; https://doi.org/10.3390/math11040991 - 15 Feb 2023
Cited by 20 | Viewed by 3978
Abstract
This article presents a hybrid backstepping consisting of two robust controllers utilizing the approximation property of a radial basis function neural network (RBFNN) for a quadrotor with time-varying uncertainties. The quadrotor dynamic system is decoupled into two subsystems: the position and the attitude [...] Read more.
This article presents a hybrid backstepping consisting of two robust controllers utilizing the approximation property of a radial basis function neural network (RBFNN) for a quadrotor with time-varying uncertainties. The quadrotor dynamic system is decoupled into two subsystems: the position and the attitude subsystems. As part of the position subsystem, adaptive RBFNN backstepping control (ANNBC) is developed to eliminate the effects of uncertainties, trace the quadrotor’s position, and provide the desired roll and pitch angles commands for the attitude subsystem. Then, adaptive RBFNN backstepping is integrated with integral fast terminal sliding mode control (ANNBIFTSMC) to track the required Euler angles and improve robustness against external disturbances. The proposed technique is advantageous because the quadrotor states trace the reference states in a short period of time without requiring knowledge of dynamic uncertainties and external disturbances. In addition, because the controller gains are based on the desired trajectories, adaptive algorithms are used to update them online. The stability of a closed loop system is proved by Lyapunov theory. Numerical simulations show acceptable attitude and position tracking performances. Full article
(This article belongs to the Topic Advances in Artificial Neural Networks)
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17 pages, 2502 KB  
Article
Low-Cost Implementation of an Adaptive Neural Network Controller for a Drive with an Elastic Shaft
by Mateusz Malarczyk, Mateusz Zychlewicz, Radoslaw Stanislawski and Marcin Kaminski
Signals 2023, 4(1), 56-72; https://doi.org/10.3390/signals4010003 - 9 Jan 2023
Cited by 6 | Viewed by 3205
Abstract
This paper deals with the implementation of an adaptive speed controller applied for two electrical machines coupled by a long shaft. The two main parts of the study are the synthesis of the neural adaptive controller and hardware implementation using a low-cost system [...] Read more.
This paper deals with the implementation of an adaptive speed controller applied for two electrical machines coupled by a long shaft. The two main parts of the study are the synthesis of the neural adaptive controller and hardware implementation using a low-cost system based on an STM Discovery board. The framework between the control system, the power converters, and the motors is established with an ARM device. A radial basis function neural network (RBFNN) is used as an adaptive speed controller. The net coefficients are updated (online mode) to ensure high dynamics of the system and correct work under disturbance. The results contain transients achieved in simulations and experimental tests. Full article
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23 pages, 5135 KB  
Article
Neural-Network-Based Terminal Sliding Mode Control of Space Robot Actuated by Control Moment Gyros
by Xinhui Xia, Yinghong Jia, Xinlong Wang and Jun Zhang
Aerospace 2022, 9(11), 730; https://doi.org/10.3390/aerospace9110730 - 19 Nov 2022
Cited by 9 | Viewed by 2673
Abstract
This paper studies the trajectory tracking control of a space robot system (SRS) in the presence of the lumped uncertainties with no prior knowledge of their upper bound. Although some related control methods have been proposed, most of them have either not been [...] Read more.
This paper studies the trajectory tracking control of a space robot system (SRS) in the presence of the lumped uncertainties with no prior knowledge of their upper bound. Although some related control methods have been proposed, most of them have either not been applied to SRSs or lack rigorous stability proof. Therefore, it is still a challenge to achieve high accuracy and rigorous theoretical proof for tracking control of SRSs. This paper proposes a new integrated neural network- based control scheme for the trajectory tracking of a SRS actuated by control moment gyros (CMGs). A new adaptive non-singular terminal sliding mode (ANTSM) control method is developed based on an improved radial basis function neural network (RBFNN). In the control method, a new weight update law is proposed to learn the upper bound of the lumped uncertainties. With the advantages of RBFNN and ANTSM, the controller has high control accuracy, fast learning speed and finite-time convergence. Different from most on-ground robotic manipulator controllers, a kinematic controller with position and attitude control laws is also designed for the satellite platform to remain stable. The stability of the closed-loop system is proved by the Lyapunov method with a high mathematical standard. Comparative simulation results demonstrate the effectiveness of the proposed control scheme with preferable performance and robustness. Full article
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23 pages, 6760 KB  
Article
Orbit-Injection Strategy and Trajectory-Planning Method of the Launch Vehicle under Power Failure Conditions
by Yin Diao, Jialun Pu, Hechuan Xu and Rongjun Mu
Aerospace 2022, 9(4), 199; https://doi.org/10.3390/aerospace9040199 - 7 Apr 2022
Cited by 2 | Viewed by 4609
Abstract
Aiming at the problem of autonomous decision making and trajectory planning (ADMTP) for launch vehicles under power failure conditions, the target degradation order strategy (TDOS) and the trajectory online planning method were studied in this paper. Firstly, the influence of power failure on [...] Read more.
Aiming at the problem of autonomous decision making and trajectory planning (ADMTP) for launch vehicles under power failure conditions, the target degradation order strategy (TDOS) and the trajectory online planning method were studied in this paper. Firstly, the influence of power failure on the orbit-injection process was analyzed. Secondly, the TDOS was proposed according to the mission attribute, failure mode, and multi-payload combination. Then, an online planning method based on the adaptive target update iterative guidance method (ATU-IGM) and radial basis neural network (RBFNN) was proposed, where the ATU-IGM adopted the basic TDOS criterion for generating optimal orbit-injection samples and online guidance instructions, and the RBFNN was used for orbit-injection samples training and online generation of orbital missions. Finally, the comparative simulation analysis was performed under multi-failure conditions. The results showed that the TDOS proposed in this paper could meet the requirements of the mission decision making under different failures, target orbit types, orbit-injection methods, and payload compositions. The online trajectory-planning capability deviation was less than 5%, and the mission decision-making and trajectory-planning time were less than 10 ms. This study provides theoretical support for autonomous decision making and planning of space launch missions. Full article
(This article belongs to the Special Issue Recent Advances in Spacecraft Dynamics and Control)
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