An improved adaptive hp mesh refinement method in solving optimal control problems

In order to improve the efficiency of the adaptive hp pseudospectral method in solving the optimal control problems, an improved adaptive hp pseudospectral method is proposed in this paper. This method mainly improves the mesh refinement process of the traditional hp pseudospectral method to reduce...

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Bibliographic Details
Published in:Optimal control applications & methods Vol. 44; no. 4; pp. 1828 - 1853
Main Authors: Luo, Changxin, Li, Jiong, Zhou, Chijun, Lei, Humin
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.07.2023
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Subjects:
Adaptive control
adaptive hp method
Efficiency
Finite element method
Grid refinement (mathematics)
mesh refinement
nonlinear programming problem
Optimal control
pseudospectral method
Spectral methods
ISSN:0143-2087, 1099-1514
Online Access:Get full text
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Summary:In order to improve the efficiency of the adaptive hp pseudospectral method in solving the optimal control problems, an improved adaptive hp pseudospectral method is proposed in this paper. This method mainly improves the mesh refinement process of the traditional hp pseudospectral method to reduce the number of mesh iterations, so as to achieve the purpose of shortening the solving time. The focus of this method is twofold. Firstly, by judging the position of the sudden change points of control curve, the mesh is refined in advance around them. Secondly, the non‐uniform segmentation iteration is carried out by using the curvature of the system state curve as the criterion. These two points together improve the solving efficiency of the proposed method. Through the convergence analysis and simulation verification, it is shown that the proposed method can effectively solve the optimal control problem, and it is also proved that the proposed method has higher solving efficiency than the traditional adaptive hp pseudospectral method.
Bibliography:Funding information
National Natural Science Foundation of China, Grant/Award Numbers: 61773398; 61873278
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0143-2087
1099-1514
DOI:10.1002/oca.2956