Fast Mesh Refinement in Pseudospectral Optimal Control
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Authors
Koeppen, N.
Ross, I.M.
Wilcox, L.C.
Proulx, R.J.
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Date of Issue
2019
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ArXiv
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Abstract
Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy: simply increase the order �� of the Lagrange interpolating polynomial, and the mathematics of convergence automates the distribution of the grid points. Unfortunately, as �� increases, the condition number of the resulting linear algebra increases as ��2; hence, spectral efficiency and accuracy are lost in practice. In this paper, Birkhoff interpolation concepts are advanced over an arbitrary grid to generate well-conditioned PS optimal control discretizations. It is shown that the condition number increases only as ��‾‾√ in general, but it is independent of �� for the special case of one of the boundary points being fixed. Hence, spectral accuracy and efficiency are maintained as �� increases. The effectiveness of the resulting fast mesh refinement strategy is demonstrated by using polynomials of over one-thousandth order to solve a low-thrust long-duration orbit transfer problem.
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Preprint
Description
The article of record as published may be found at https://doi.org/10.2514/1.G003904
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Department
Mechanical and Aerospace Engineering (MAE)
Applied Mathematics
Space Systems Academic Group
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27 p.
Citation
Koeppen, N., et al. "Fast mesh refinement in pseudospectral optimal control." Journal of Guidance, Control, and Dynamics 42.4 (2019): 711-722.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.