An hp mesh refinement method for optimal control using discontinuity detection and mesh size reduction

2014 ◽  
Author(s):  
Fengjin Liu ◽  
William W. Hager ◽  
Anil V. Rao
Keyword(s):  
Optimal Control ◽  
Mesh Refinement ◽  
Mesh Size ◽  
Size Reduction ◽  
Discontinuity Detection ◽  
Refinement Method

scholarly journals An Improved Adaptive hp Mesh Refinement Method in Solving Optimal Control Problems

2021 ◽  
Author(s):  
Changxin Luo ◽  
Jiong Li ◽  
Chijun Zhou ◽  
Humin Lei
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Computing Time ◽  
Mesh Refinement ◽  
Pseudospectral Method ◽  
Change Rate ◽  
Refinement Method ◽  
Effective Choice

Abstract The adaptive hp pseudospectral method is an effective choice in solving the optimal control problem. In order to improve the computing efficiency of the adaptive hp method, an improved adaptive hp mesh refinement method is proposed in this paper. There are two main cores in this method. The first is to refine the mesh in advance based on the change rate of the control, so that the algorithm can more efficiently deal with the optimal control problem with discontinuous control. And the second is to based on the accumulation of curvature values to ensure that those positions that need to be refined more can be quickly allocated to more mesh points. These two are combined with each other to improve the solving efficiency of the algorithm proposed in this paper, which shortens the required computing time. In addition, the convergence of the algorithm is proved in this paper. The simulation results show the effectiveness and superiority of the algorithm proposed in this paper.

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