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Adaptive mesh refinement method for solving optimal control problems using interpolation error analysis and improved data compression
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DOI：10.1016/j.jfranklin.2019.11.024.png)
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This paper presents a simple and efficient adaptive mesh refinement method for solving optimal control problems using direct methods. The method inserts new points into the mesh by successively subdividing the neighboring intervals around each mesh point where the interpolation error exceeds a prescribed threshold. The unnecessary points in the mesh are removed by the use of an improved data compression method based on generalized dyadic meshes. Furthermore, to further reduce the mesh size, the method allows the use of the neighboring mesh points of both lower and higher resolution levels (i.e., it uses more information in the mesh) when calculating the interpolation error in the mesh point insertion and compression procedures. The method is demonstrated with four examples, and its performance is compared against that of several other recently developed adaptive mesh refinement methods for optimal control reported in the literature. The numerical results show that the proposed method has advantages over other methods because it achieves the same or a more accurate solution while producing smaller mesh sizes and even requiring fewer mesh iterations than other methods. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
Keyword:
DIRECT TRAJECTORY OPTIMIZATION
DYNAMIC OPTIMIZATION
PARAMETERIZATION APPROACH
PSEUDOSPECTRAL METHODS
TIME OPTIMIZATION
SQP ALGORITHM
SNOPT
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1.5W
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