scholarly journals A vector field method on the distorted Fourier side and decay for wave equations with potentials

2016 ◽  
Vol 241 (1142) ◽  
pp. 0-0 ◽  
Author(s):  
Roland Donninger ◽  
Joachim Krieger
Keyword(s):  
Vector Field ◽  
Wave Equations ◽  
Field Method ◽  
Vector Field Method

scholarly journals Modified Vector Field Path-Following Control System for an Underactuated Autonomous Surface Ship Modelin the Presence of Static Obstacles

2021 ◽  
Vol 9 (6) ◽  
pp. 652
Author(s):  
Haitong Xu ◽  
Miguel A. Hinostroza ◽  
C. Guedes Guedes Soares
Keyword(s):  
Control System ◽  
Vector Field ◽  
Path Following ◽  
Field Method ◽  
Integrated System ◽  
Ship Model ◽  
Surface Ship ◽  
Path Following Control ◽  
Exponentially Stable ◽  
Vector Field Method

A modified path-following control system using the vector field method for an underactuated autonomous surface ship model is proposed in the presence of static obstacles. With this integrated system, autonomous ships are capable of following the predefined path, while avoiding the obstacles automatically. It is different from the methods in most published papers, which usually study path-following and obstacle collision avoidance, separately. This paper considers the coupled path following and collision avoidance task as a whole. Meanwhile, the paper also shows the heading control design method in the presence of static obstacles. To obtain a strong stability property, a nonlinear autopilot is designed based on the manoeuvring tests of the free-running ship model. The equilibrium point of the controller is globally exponentially stable. For the guidance system, a novel vector field method was proposed, and the proof shows the coupled guidance and control system is uniform semi-global exponentially stable (USGES). To prevent the obstacles near the predefined path, the proposed guidance law is augmented by integrating the repelling field of obstacles so that it can control the ship travel toward the predefined path through the obstacles safely. The repelling field function is given considering the obstacle shape and collision risk using the velocity obstacle (VO) algorithm. The simulations and ship model test were performed to validate the integrated system of autonomous ships.

scholarly journals A vector field method for relativistic transport equations with applications

2017 ◽  
Vol 10 (7) ◽  
pp. 1539-1612 ◽  
Author(s):  
David Fajman ◽  
Jérémie Joudioux ◽  
Jacques Smulevici
Keyword(s):  
Vector Field ◽  
Field Method ◽  
Transport Equations ◽  
Vector Field Method
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