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Journal articles on the topic 'Trajectory convergence'

Author: Grafiati

Published: 23 November 2024

Last updated: 31 July 2025

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1

Kuzmenko, Viktor. "Trajectory convergence." Cybernetics and Computer Technologies, no. 4 (March 18, 2025): 5–12. https://doi.org/10.34229/2707-451x.25.1.1.

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2

Ning, Tan, Zhang Yun-Jun, Ouyang Qi, and Geng Zhi. "Dynamical Convergence Trajectory in Networks." Chinese Physics Letters 22, no. 9 (2005): 2447–50. http://dx.doi.org/10.1088/0256-307x/22/9/085.

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3

Deng, Jiao-Jiao, Hsiao-Dong Chiang, and Tian-Qi Zhao. "Newton Method and Trajectory-Based Method for Solving Power Flow Problems: Nonlinear Studies." International Journal of Bifurcation and Chaos 25, no. 06 (2015): 1530018. http://dx.doi.org/10.1142/s0218127415300189.

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This paper analyzes the convergence properties and convergence region of a class of trajectory-based power flow methods. The convergence region of the trajectory-based method is a connected set and possesses the near-by property. The convergence region of Newton method and trajectory-based method in solving power flow problems are numerically investigated. Since the convergence region of trajectory-based method corresponds to the stability region of the nonlinear dynamic system, the stability regions of two dynamic systems are computed. The numerical results indicate that the stability region

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4

Xia, Youshen, and Gang Feng. "On Convergence Conditions of an Extended Projection Neural Network." Neural Computation 17, no. 3 (2005): 515–25. http://dx.doi.org/10.1162/0899766053019926.

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The output trajectory convergence of an extended projection neural network was developed under the positive definiteness condition of the Jacobian matrix of nonlinear mapping. This note offers several new convergence results. The state trajectory convergence and the output trajectory convergence of the extended projection neural network are obtained under the positive semidefiniteness condition of the Jacobian matrix. Comparison and illustrative examples demonstrate applied significance of these new results.

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5

Fang, Zheng, and Qing Li. "Fixed-time INDI control for UAV trajectory tracking." Journal of Physics: Conference Series 3026, no. 1 (2025): 012026. https://doi.org/10.1088/1742-6596/3026/1/012026.

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Abstract The trajectory tracking control of fixed-wing Unmanned Aerial Vehicles (UAVs) is inherently challenging due to their nonlinear, underactuated, and strongly coupled dynamics, as well as their vulnerability to external perturbations. This paper introduces an incremental nonlinear dynamic inversion (INDI) control method with fixed-time convergence for the design of both attitude and guidance law for UAVs. The proposed control method’s robustness and rapid response are validated through simulation experiments using a high-precision UAV model in Simulink. The method outperforms traditional

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6

Xu, Liu, Wei Min Li, Lin Zhang, and An Tang Zhang. "The Applications of Improved Genetic Algorithm on Hypersonic Vehicle Trajectory Optimization." Advanced Materials Research 466-467 (February 2012): 1095–99. http://dx.doi.org/10.4028/www.scientific.net/amr.466-467.1095.

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The Optimal trajectory design for hypersonic cruise missile is an optimal control problem with strict terminal constraints and variable final time. The classical algorithms always encounter the problems of high sensitivity to initial guess and local convergence in solving this problem. Aiming at these problems, genetic algorithm (GA) which is of good global convergence is applied to designing the optimal trajectory for hypersonic cruise missile. In order to improve the convergence rate of GA and overcome its premature problems, this text introduces a predatory search (PS) strategy to speed the

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Gan, Wenyang, Tianxing Xia, and Zhenzhong Chu. "A Prognosis Technique Based on Improved GWO-NMPC to Improve the Trajectory Tracking Control System Reliability of Unmanned Underwater Vehicles." Electronics 12, no. 4 (2023): 921. http://dx.doi.org/10.3390/electronics12040921.

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The dynamics model of the unmanned underwater vehicle (UUV) system is highly nonlinear, multi-degree-of-freedom, strongly coupled, and time-varying. Its motion control has been a complex problem due to the unknown information about and the uncertainty of the working environment. To improve the performance and reliability of UUV trajectory tracking control, a trajectory tracking method based on nonlinear model predictive control is designed, and an improved gray wolf optimization (IGWO) is proposed for the optimization of nonlinear model predictive control. The convergence factor of IGWO is des

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8

Dubanov, A. A. "Kinematic model of the parallel convergence method in space." Journal of Physics: Conference Series 2182, no. 1 (2022): 012004. http://dx.doi.org/10.1088/1742-6596/2182/1/012004.

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Abstract In this article, the implementation of the method of parallel convergence in space in a computer mathematics system is considered and discussed. In this method, the pursuer’s velocity vector is directed arbitrarily. The pursuer’s trajectory gradually approaches movement in the plane formed by the line connecting the initial positions of the pursuer and the target, and the velocity vector. In this task, the target moves uniformly and rectilinearly. The pursuer moves evenly. The points of the pursuer’s trajectory are calculated sequentially. They are being the result of the intersection

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9

Ling, Guo, Du Weiwei, Yang Jiancheng, Wang Liping, Wan Ping, and Liu Ling. "A Thermal Load Forecasting Algorithm Based on Trajectory Tracking." Mathematical Problems in Engineering 2020 (November 16, 2020): 1–12. http://dx.doi.org/10.1155/2020/5919238.

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The heating load forecast provides a basis for saving heating energy. Considering the nonstationary, nonlinear, and large time-delay characteristics of thermal load, this paper introduces the trajectory tracking stability theory into the field of load forecasting and proposes a heuristic correction that can ensure the convergence of forecast errors and does not depend on the system prediction model algorithm. The Lyapunov method is used to derive an error convergence criterion that has nothing to do with the prediction model, and a heuristic correction algorithm is designed for the predicted v

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10

Huang, Hangjie, and Jinfeng Gao. "Backstepping and Novel Sliding Mode Trajectory Tracking Controller for Wheeled Mobile Robots." Mathematics 12, no. 10 (2024): 1458. http://dx.doi.org/10.3390/math12101458.

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A novel variable structure controller based on sliding mode is developed for addressing the trajectory tracking challenge encountered by wheeled mobile robots. Firstly, the trajectory tracking error model under the global coordinate system is established according to the kinematic model of the wheeled mobile robot. Secondly, the novel sliding mode algorithm and backstepping method are introduced to design the motion controller of the system, respectively. Different sliding mode surfaces are formulated to guarantee rapid and stable convergence of the system’s trajectory tracking error to zero.

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11

Sun, Hanqing, Shijie Zhang, Qingle Quan, Zheng Liu, Guizhi Wang, and Weimin Lian. "Trajectory Tracking Robust Control Method Based on Finite-Time Convergence of Manipulator with Nonsingular Fast Terminal Sliding Mode Surface." Journal of Control Science and Engineering 2022 (April 7, 2022): 1–9. http://dx.doi.org/10.1155/2022/2271804.

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In order to make the manipulator track the desired trajectory in a finite time, a new control method based on fast nonsingular terminal sliding mode has been designed. This method combines the traditional fast terminal sliding mode with the nonsingular terminal sliding mode, has rapidity, nonsingularity, finite-time convergence, and strong robustness, and can effectively suppress the inherent chattering phenomenon of the sliding mode controller. The nonsingular fast terminal sliding mode surface is used to accelerate the convergence speed of manipulator trajectory tracking error, and the singu

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Zheng, Xu, Liang He, Wei Wei, and Haosheng Wang. "Research on the Aerodynamic and External Ballistic Characteristics of Bullets Based on Low-Temperature Meteorological Factors." Journal of Physics: Conference Series 2891, no. 16 (2024): 162008. https://doi.org/10.1088/1742-6596/2891/16/162008.

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Abstract To further investigate the aerodynamic and ballistic trajectory characteristics of a certain type of ammunition under the influence of low-temperature meteorological factors, based on computational fluid dynamics and rigid body dynamic trajectory equations, numerical calculations and analysis of the aerodynamic characteristics and 6-degree-of-freedom rigid body ballistic trajectory, as well as low-temperature environmental ballistic trajectory flight tests, were conducted on this type of ammunition. The research shows that under constant atmospheric pressure, as the ambient temperatur

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13

Liu, Junjie, Hui Wang, Xue Li, Kai Chen, and Chaoyu Li. "Robotic arm trajectory optimization based on multiverse algorithm." Mathematical Biosciences and Engineering 20, no. 2 (2022): 2776–92. http://dx.doi.org/10.3934/mbe.2023130.

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<abstract><p>For inefficient trajectory planning of six-degree-of-freedom industrial manipulators, a trajectory planning algorithm based on an improved multiverse algorithm (IMVO) for time, energy, and impact optimization are proposed. The multi-universe algorithm has better robustness and convergence accuracy in solving single-objective constrained optimization problems than other algorithms. In contrast, it has the disadvantage of slow convergence and quickly falls into local optimum. This paper proposes a method to improve the wormhole probability curve, adaptive parameter adjus

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14

Qiu, Shi Ying, Peng Yi, Rui Bo Yuan, Huan Yang, Sen Hui, and Rong Ping Xue. "Trajectory Control for Cartesian Pneumatic Manipulator Using the Terminal Sliding Mode Control Method." Applied Mechanics and Materials 444-445 (October 2013): 1354–59. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.1354.

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This paper applies the terminal sliding mode control method to control the trajectory of a three axises Cartesian Pneumatic Manipulator. A mathematical model of the pneumatic servo control system was established at first, then the terminal sliding mode control method was used for trajectory control. The simulation results shows that the tracking error of the terminal sliding mode control method become large only in the time period of not fully reaching the convergence point in time when the manipulator tracks the space straight line, whereas it can fully track the target trajectory after reach

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15

Bigras, Pascal, Maarouf Saad, and Jules O'shea. "Convergence Analysis of an Inverse Flexible Manipulator Model Algorithm." Journal of Vibration and Control 9, no. 10 (2003): 1141–58. http://dx.doi.org/10.1177/107754603030705.

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In this paper we present a convergence analysis of an iterative method to obtain the inverse model in the virtual joint space of a class of flexible manipulators. Virtual joints are defined so as to be related kinematically to the workspace. Thus, when the desired trajectory can be transformed from the workspace to the virtual joint space, the inverse model in the virtual joint space can be used to obtain a trajectory tip-tracking controller. Because the robot model in the virtual joint space is a non-minimum phase system, its inverse is unstable. The inverse method is then based on a causal-a

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16

Zhai, Guanyu, Jundong Zhang, Shuyun Wu, and Yongkang Wang. "Predefined-Time Tracking Control of Unmanned Surface Vehicle under Complex Time-Varying Disturbances." Electronics 13, no. 8 (2024): 1510. http://dx.doi.org/10.3390/electronics13081510.

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Aiming at the unmanned surface vehicle (USV) trajectory tracking control under complex time-varying environment, a predefined-time convergence sliding mode disturbance observer (PTC-SMO) is introduced to effectively handle the internal parameter uncertainties and external environmental disturbances, thereby guaranteeing precise compensation of the lumped disturbance term within a set time. Then, in order to achieve precise tracking of the desired trajectory using USV under a predetermined time constraint, a novel fast trajectory tracking control strategy with predefined-time convergence (PTC-F

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17

Xu, Huiyan, Guoqing Zhai, and Xiaofan Li. "Precipitation Efficiency and Water Budget of Typhoon Fitow (2013): A Particle Trajectory Study." Journal of Hydrometeorology 18, no. 9 (2017): 2331–54. http://dx.doi.org/10.1175/jhm-d-16-0273.1.

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Abstract In this study, the WRF Model is used to simulate the torrential rainfall of Typhoon Fitow (2013) over coastal areas of east China during its landfall. Data from the innermost model domain are used to trace trajectories of particles in three major 24-h accumulated rainfall centers using the Lagrangian flexible particle dispersion model (FLEXPART). Surface rainfall budgets and cloud microphysical budgets as well as precipitation efficiency are analyzed along the particles’ trajectories. The rainfall centers with high precipitation efficiency are associated with water vapor convergence,

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18

Gu, Haipeng, Tie Yan, and Yang Wu. "Research on Intelligent Optimization of Wellbore Trajectory in Complex Formation." Applied Sciences 15, no. 3 (2025): 1364. https://doi.org/10.3390/app15031364.

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Borehole trajectory optimization is a key issue in oil and gas drilling engineering. The traditional wellbore trajectory design method faces great challenges in optimizing the trajectory length and complexity, and it is difficult to meet the actual engineering requirements. In this paper, the three-stage wellbore trajectory optimization problem is studied, and a multi-objective optimization model including two objective functions of trajectory length and trajectory complexity is constructed. In this paper, an improved multi-objective particle swarm optimization algorithm is proposed, which com

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19

Boţ, Radu Ioan, and Dang-Khoa Nguyen. "Improved convergence rates and trajectory convergence for primal-dual dynamical systems with vanishing damping." Journal of Differential Equations 303 (December 2021): 369–406. http://dx.doi.org/10.1016/j.jde.2021.09.021.

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20

Liang, Haizhao, Yunhao Luo, Haohui Che, Jingxian Zhu, and Jianying Wang. "A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers." Mathematics 12, no. 9 (2024): 1306. http://dx.doi.org/10.3390/math12091306.

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The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex

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21

Hota, Sikha, and Debasish Ghose. "Optimal Trajectory Generation for Convergence to a Rectilinear Path." Journal of Intelligent & Robotic Systems 75, no. 2 (2013): 223–42. http://dx.doi.org/10.1007/s10846-013-9863-1.

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22

Seibert, Petra. "Convergence and Accuracy of Numerical Methods for Trajectory Calculations." Journal of Applied Meteorology 32, no. 3 (1993): 558–66. http://dx.doi.org/10.1175/1520-0450(1993)032<0558:caaonm>2.0.co;2.

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23

Ljubich, Yu I. "On trajectory convergence of dissipative flows in Banach spaces." Integral Equations and Operator Theory 13, no. 1 (1990): 138–44. http://dx.doi.org/10.1007/bf01195297.

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24

Tenne, Yoel. "Accelerating the Convergence of Evolutionary Algorithms by Trajectory Analysis." Journal of Physics: Conference Series 3027, no. 1 (2025): 012037. https://doi.org/10.1088/1742-6596/3027/1/012037.

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Abstract Evolutionary algorithms are heuristic nature-inspired search methods based on the concepts of adaptation and survival of the fittest. While they have proven to be effective across varied problems they are often inefficient, namely, they may be slow to converge and require a large number of function evaluations to yield a satisfactory solution. To address these issues this paper proposes a new algorithm to accelerate the EA convergence based on the trajectory traversed by the EA population during the search. Based on this trajectory a vector is derived which approximately points to an

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Li, Ningbo, Humin Lei, Lei Shao, Tao Liu, and Bin Wang. "Trajectory Optimization Based on Multi-Interval Mesh Refinement Method." Mathematical Problems in Engineering 2017 (2017): 1–8. http://dx.doi.org/10.1155/2017/8521368.

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In order to improve the optimization accuracy and convergence rate for trajectory optimization of the air-to-air missile, a multi-interval mesh refinement Radau pseudospectral method was introduced. This method made the mesh endpoints converge to the practical nonsmooth points and decreased the overall collocation points to improve convergence rate and computational efficiency. The trajectory was divided into four phases according to the working time of engine and handover of midcourse and terminal guidance, and then the optimization model was built. The multi-interval mesh refinement Radau ps

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K. Wilburn, Brenton, Mario G. Perhinschi, and Jennifer N. Wilburn. "A modified genetic algorithm for UAV trajectory tracking control laws optimization." International Journal of Intelligent Unmanned Systems 2, no. 2 (2014): 58–90. http://dx.doi.org/10.1108/ijius-03-2014-0002.

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Purpose – The purpose of this paper is to gain trajectory-tracking controllers for autonomous aircraft are optimized using a modified evolutionary, or genetic algorithm (GA). Design/methodology/approach – The GA design utilizes real representation for the individual consisting of the collection of all controller gains subject to tuning. The initial population is generated randomly over pre-specified ranges. Alternatively, initial individuals are produced as random variations from a heuristically tuned set of gains to increase convergence time. A two-point crossover mechanism and a probabilisti

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Cui, Hong, and Chongwen Yu. "A Mathematical Model for Self-Twist Yarn Spinning Process." Research Journal of Textile and Apparel 18, no. 1 (2014): 1–5. http://dx.doi.org/10.1108/rjta-18-01-2014-b001.

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A mathematical model is established for self-twist spinning process by applying laws of fluid mechanics (i.e. mass conservation and momentum conservation). The motion curve of the convergent point was determined and the convergence point was decided by densities and velocities of two fed-in strands and the resultant self-twist yarn, independent of their mechanical properties. The experimental verification proves that the motion trajectory of the convergence point reaches a better agreement with the theoretical trajectory. The results provide general way to study the self-twist yarn spinning pr

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Xie, Jian, Yongquan Zhou, and Huan Chen. "A Novel Bat Algorithm Based on Differential Operator and Lévy Flights Trajectory." Computational Intelligence and Neuroscience 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/453812.

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Aiming at the phenomenon of slow convergence rate and low accuracy of bat algorithm, a novel bat algorithm based on differential operator and Lévy flights trajectory is proposed. In this paper, a differential operator is introduced to accelerate the convergence speed of proposed algorithm, which is similar to mutation strategy “DE/best/2” in differential algorithm. Lévy flights trajectory can ensure the diversity of the population against premature convergence and make the algorithm effectively jump out of local minima. 14 typical benchmark functions and an instance of nonlinear equations are

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Chen, Shuo, Jiaying Peng, Xiaolong Li, and Yao Zhao. "On the Unstable Convergence Regime of Gradient Descent." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 10 (2024): 11373–80. http://dx.doi.org/10.1609/aaai.v38i10.29017.

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Traditional gradient descent (GD) has been fully investigated for convex or L-smoothness functions, and it is widely utilized in current neural network optimization. The classical descent lemma ensures that for a function with L-smoothness, the GD trajectory converges stably towards the minimum when the learning rate is below 2 / L. This convergence is marked by a consistent reduction in the loss function throughout the iterations. However, recent experimental studies have demonstrated that even when the L-smoothness condition is not met, or if the learning rate is increased leading to oscilla

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Lee, Jonathan N., Michael Laskey, Ajay Kumar Tanwani, Anil Aswani, and Ken Goldberg. "Dynamic regret convergence analysis and an adaptive regularization algorithm for on-policy robot imitation learning." International Journal of Robotics Research 40, no. 10-11 (2021): 1284–305. http://dx.doi.org/10.1177/0278364920985879.

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On-policy imitation learning algorithms such as DAgger evolve a robot control policy by executing it, measuring performance (loss), obtaining corrective feedback from a supervisor, and generating the next policy. As the loss between iterations can vary unpredictably, a fundamental question is under what conditions this process will eventually achieve a converged policy. If one assumes the underlying trajectory distribution is static (stationary), it is possible to prove convergence for DAgger. However, in more realistic models for robotics, the underlying trajectory distribution is dynamic bec

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Wang, Feng Bo, and Chang Hong Dong. "Coevolutionary Algorithm Applied to Skip Reentry Trajectory Optimization Design." Applied Mechanics and Materials 427-429 (September 2013): 1424–31. http://dx.doi.org/10.4028/www.scientific.net/amm.427-429.1424.

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This paper proposed a coevolutionary algorithm combining improved particle swarm optimization algorithm with differential evolution method and its application was provided. Adaptive position escapable mechanism is introduced in the particle swarm optimization to improve the diversity of population and guarantee to achieve the global optima. The differential algorithm is employed in a cooperative manner to maintain the characteristic of fast convergence speed in the later convergence phase. The coevolutionary algorithm is then applied to skip trajectory optimization design for crew exploration

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32

Velasco–Villa, M., A. Rodriguez–Angeles, I. Z. Maruri–López, J. A. Báez-Hernández, and R. D. Cruz Morales. "Leader–follower formation control based on non-inertial frames for non–holonomic mobile robots." PLOS ONE 19, no. 1 (2024): e0297061. http://dx.doi.org/10.1371/journal.pone.0297061.

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A chain formation strategy based on mobile frames for a set of n differential drive mobile robots is presented. Considering two consecutive robots in the formation, robots Ri and Ri+1. It is intended that robot Ri+1 follows the delayed trajectory, τ units of time, of the leader robot Ri. In this way, the follower robot Ri+1 becomes the leader robot for robot Ri+ 2 in the formation and so on. With this formation policy, the trailing distance between two consecutive robots varies accordingly to the velocity of the Ri leader robot. Mobile frames are located on the body of the vehicles, in such a

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Chen, Jie, Jiace Yuan, and Ruohan Li. "Error-Constrained Fixed-Time Synchronized Trajectory Tracking Control for Unmanned Airships with Disturbances." Drones 9, no. 6 (2025): 403. https://doi.org/10.3390/drones9060403.

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This work focuses on fixed-time synchronized trajectory tracking control for unmanned airships subject to time-varying error constraints and unknown disturbances. First, to guarantee strict adherence to prescribed performance bounds, an error transformation function (ETF) is integrated into the control algorithm, which can ensure all tracking errors remain within specified constraints throughout the convergence process. Then, a Norm-Normalized sign (NNS) function is incorporated to develop the control scheme, guaranteeing simultaneous convergence of all tracking error components. Additionally,

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Azhmoldaev, Gaziz F., Kuanysh A. Bekmaganbetov, Gregory A. Chechkin, and Vladimir V. Chepyzhov. "Homogenization of attractors to reaction–diffusion equations in domains with rapidly oscillating boundary: Critical case." Networks and Heterogeneous Media 19, no. 3 (2024): 1381–401. https://doi.org/10.3934/nhm.2024059.

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<p>In the present paper, reaction–diffusion systems (RD-systems) with rapidly oscillating coefficients and righthand sides in equations and in boundary conditions were considered in domains with locally periodic oscillating (wavering) boundary. We proved a weak convergence of the trajectory attractors of the given systems to the trajectory attractors of the limit (homogenized) RD-systems in domain independent of the small parameter, characterizing the oscillation rate. We consider the critical case in which the type of boundary condition was preserved. For this aim, we used the approach

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Panahandeh, Pouya, Khalil Alipour, Bahram Tarvirdizadeh, and Alireza Hadi. "A self-tuning trajectory tracking controller for wheeled mobile robots." Industrial Robot: the international journal of robotics research and application 46, no. 6 (2019): 828–38. http://dx.doi.org/10.1108/ir-02-2019-0032.

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Purpose Trajectory tracking is a common problem in the field of mobile robots which has attracted a lot of attention in the past two decades. Therefore, besides the search for new controllers to achieve a better performance, improvement and optimization of existing control rules are necessary. Trajectory tracking control laws usually contain constant gains which affect greatly the robot’s performance. Design/methodology/approach In this paper, a method based on neural networks is introduced to automatically upgrade the gains of a well-known trajectory tracking controller of wheeled mobile robo

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Liu, Lei, Yongji Wang, Fuqiang Xie, and Jiashi Gao. "Legendre Cooperative PSO Strategies for Trajectory Optimization." Complexity 2018 (2018): 1–13. http://dx.doi.org/10.1155/2018/5036791.

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Particle swarm optimization (PSO) is a population-based stochastic optimization technique in a smooth search space. However, in a category of trajectory optimization problem with arbitrary final time and multiple control variables, the smoothness of variables cannot be satisfied since the linear interpolation is widely used. In the paper, a novel Legendre cooperative PSO (LCPSO) is proposed by introducing Legendre orthogonal polynomials instead of the linear interpolation. An additional control variable is introduced to transcribe the original optimal problem with arbitrary final time to the f

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Zheng, Minjie, Qianqiang Chen, Yulai Su, and Guoquan Chen. "Sustainable Trajectory Tracking Control for Underactuated Ships Using Non-Singular Fast Terminal Sliding Mode Control." Sustainability 17, no. 13 (2025): 5866. https://doi.org/10.3390/su17135866.

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Accurate and robust trajectory tracking is essential for ensuring the safety and efficiency of underactuated ships operating in complex marine environments. However, conventional sliding mode control (SMC) methods often suffer from issues such as chattering and slow convergence, limiting their practical application. To address these challenges, this paper proposes a novel non-singular fast terminal sliding mode control (NFTSMC) strategy for sustainable trajectory tracking of underactuated ships. The proposed approach first designs a virtual control law based on surge and sway position errors,

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Kozera, Ryszard. "Asymptotics for Length and Trajectory from Cumulative Chord Piecewise-Quartics." Fundamenta Informaticae 61, no. 3-4 (2004): 267–83. https://doi.org/10.3233/fun-2004-613-405.

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We discuss the problem of estimating the trajectory of a regular curve γ:[0,T]→Rn and its length d(γ) from an ordered sample of interpolation points Qm={γ(t0),γ(t1),...,γ(tm)}, with tabular points ti's unknown, coined as interpolation of unparameterized data. The respective convergence orders for estimating γ and d(γ) with cumulative chord piecewise-quartics are established for different types of unparameterized data including egr-uniform and more-or-less uniform samplings. The latter extends previous results on cumulative chord piecewise-quadratics and piecewise-cubics. As shown herein, furth

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Xu, Lixin, Jiarong Chen, Zhichao Hong, Shengqing Xu, Sheng Zhang, and Lin Shi. "Research on Ship Trajectory Control Based on Deep Reinforcement Learning." Journal of Marine Science and Engineering 13, no. 4 (2025): 792. https://doi.org/10.3390/jmse13040792.

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Ship trajectory tracking controllers based on deep reinforcement learning (DRL) are widely applied in various fields such as autonomous driving and robotics due to their strong adaptive learning capabilities and optimization decision-making ability. However, ship trajectory control faces challenges such as long training cycles and poor convergence performance. These issues are primarily caused by the unreasonable design of algorithm models and reward functions, which limit the performance optimization and energy efficiency improvements in real-world navigation. In this paper, we propose a ship

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Bekmaganbetov, Kuanysh A., Gregory A. Chechkin, and Vladimir V. Chepyzhov. "Application of Fatou’s Lemma for Strong Homogenization of Attractors to Reaction–Diffusion Systems with Rapidly Oscillating Coefficients in Orthotropic Media with Periodic Obstacles." Mathematics 11, no. 6 (2023): 1448. http://dx.doi.org/10.3390/math11061448.

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We study reaction–diffusion systems with rapidly oscillating terms in the coefficients of equations and in the boundary conditions, in media with periodic obstacles. The non-linear terms of the equations only satisfy general dissipation conditions. We construct trajectory attractors for such systems in the strong topology of the corresponding trajectory dynamical systems. By means of generalized Fatou’s lemma we prove the strong convergence of the trajectory attractors of considered systems to the trajectory attractors of the corresponding homogenized reaction–diffusion systems which contain a

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Fan, Siwen, Wanli Li, and Rui Xie. "Self-tuning trajectory tracking control for concrete pouring construction robots based on PID-NFTSMC and CPO algorithm." PLOS One 20, no. 5 (2025): e0324550. https://doi.org/10.1371/journal.pone.0324550.

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This paper presented a self-tuning trajectory tracking control strategy for concrete pouring construction robots operating under external disturbances and system uncertainties. To enhance operational stability and robustness, the study integrated proportional-integral-derivative (PID) control with nonsingular fast terminal sliding mode control (NFTSMC), enabling faster convergence to the desired trajectory and reduced steady-state errors. Additionally, the study employed the crested porcupine optimizer (CPO) algorithm to automatically optimize PID control gains and NFTSMC sliding surface param

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Shi, Junren, Kexin Li, Changhao Piao, Jun Gao, and Lizhi Chen. "Model-Based Predictive Control and Reinforcement Learning for Planning Vehicle-Parking Trajectories for Vertical Parking Spaces." Sensors 23, no. 16 (2023): 7124. http://dx.doi.org/10.3390/s23167124.

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This paper proposes a vehicle-parking trajectory planning method that addresses the issues of a long trajectory planning time and difficult training convergence during automatic parking. The process involves two stages: finding a parking space and parking planning. The first stage uses model predictive control (MPC) for trajectory tracking from the initial position of the vehicle to the starting point of the parking operation. The second stage employs the proximal policy optimization (PPO) algorithm to transform the parking behavior into a reinforcement learning process. A four-dimensional rew

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Huang, Shurui, Yueneng Yang, Ye Yan, Shifeng Zhang, and Zhiyang Liu. "Observer-Based Robust Finite-Time Trajectory Tracking Control for a Stratospheric Satellite Subject to External Disturbance and Actuator Saturation." International Journal of Aerospace Engineering 2022 (September 29, 2022): 1–19. http://dx.doi.org/10.1155/2022/1601771.

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The stratospheric satellite is regarded as an ideal stratosphere flight platform and is able to accomplish various missions such as surveillance, earth observation, and remote sensing, which requires a robust and effective trajectory tracking control method to support these tasks. A novel observer-based robust finite-time control scheme is proposed to address the trajectory tracking control problem dedicated to a stratospheric satellite in the presence of external disturbance and actuator saturation. Firstly, an extended state observer (ESO) is adopted to observe the unavailable velocity state

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Dai, Xiaoqiang, Hewei Xu, Hongchao Ma, Jianjun Ding, and Qiang Lai. "Dual closed loop AUV trajectory tracking control based on finite time and state observer." Mathematical Biosciences and Engineering 19, no. 11 (2022): 11086–113. http://dx.doi.org/10.3934/mbe.2022517.

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<abstract><p>The three-dimensional trajectory tracking of AUV is an important basis for it to complete its task. Due to many uncertain disturbances such as wind, wave and current on the sea, it is easy to cause problems such as slow convergence speed of the controller and saturation of the controller output in the three-dimensional trajectory tracking control of AUV. And the dynamic uncertainty of AUV's own model will have a great negative impact on AUV's trajectory tracking control. In order to solve the problem of slow convergence speed of the above controller, the finite time co

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Zhang, Biao. "Quadrotor Convergence Trajectory Optimization Model Based on Minimum Energy Consumption." Advances in Applied Mathematics and Mechanics 10, no. 3 (2018): 673–89. http://dx.doi.org/10.4208/aamm.oa-2017-0059.

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Bansal, Jagdish Chand, Anshul Gopal, and Atulya K. Nagar. "Analysing Convergence, Consistency, and Trajectory of Artificial Bee Colony Algorithm." IEEE Access 6 (2018): 73593–602. http://dx.doi.org/10.1109/access.2018.2884255.

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Hota, Sikha, and Debasish Ghose. "Optimal trajectory planning for path convergence in three-dimensional space." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 228, no. 5 (2013): 766–80. http://dx.doi.org/10.1177/0954410013479714.

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Hendrickx, Julien M., and Balázs Gerencsér. "Trajectory convergence from coordinate-wise decrease of general energy functions." Automatica 154 (August 2023): 111099. http://dx.doi.org/10.1016/j.automatica.2023.111099.

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Luo, Lan, Tongbin Guo, Kangkang Cui, and Qi Zhang. "Trajectory Planning in Robot Joint Space Based on Improved Quantum Particle Swarm Optimization Algorithm." Applied Sciences 13, no. 12 (2023): 7031. http://dx.doi.org/10.3390/app13127031.

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Trajectory planning is a crucial step in controlling robot motion. The efficiency and accuracy of trajectory planning directly impact the real-time control and accuracy of robot motion. The robot’s trajectory is mapped to the joint space, and a mathematical model of trajectory planning is established to meet physical constraints during motion and avoid joint coupling problems. To enhance convergence speed and avoid local optima, an improved quantum particle swarm optimization algorithm is proposed and applied to solve the mathematical model of robot trajectory planning. The trajectory planning

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KE, YIFEN, and CHANGFENG MA. "A NEURAL NETWORK FOR THE GENERALIZED NONLINEAR COMPLEMENTARITY PROBLEM OVER A POLYHEDRAL CONE." Journal of the Australian Mathematical Society 99, no. 3 (2015): 364–79. http://dx.doi.org/10.1017/s1446788715000300.

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In this paper, we consider a neural network model for solving the generalized nonlinear complementarity problem (denoted by GNCP) over a polyhedral cone. The neural network is derived from an equivalent unconstrained minimization reformulation of the GNCP, which is based on the penalized Fischer–Burmeister function ${\it\phi}_{{\it\mu}}(a,b)={\it\mu}{\it\phi}_{\mathit{FB}}(a,b)+(1-{\it\mu})a_{+}b_{+}$. We establish the existence and the convergence of the trajectory of the neural network, and study its Lyapunov stability, asymptotic stability and exponential stability. It is found that a large

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