Publication:
Fast Mesh Refinement in Pseudospectral Optimal Control

Loading...
Thumbnail Image
Authors
Koeppen, N.
Ross, I.M.
Wilcox, L.C.
Proulx, R.J.
Subjects
Advisors
Date of Issue
2019
Date
Publisher
ArXiv
Language
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.
Type
Preprint
Description
The article of record as published may be found at https://doi.org/10.2514/1.G003904
Series/Report No
Department
Mechanical and Aerospace Engineering (MAE)
Applied Mathematics
Space Systems Academic Group
Organization
Identifiers
NPS Report Number
Sponsors
Funder
Format
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.
Distribution Statement
Rights
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.
Collections