Fast Mesh Refinement in Pseudospectral Optimal Control

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Tác giả: N Koeppen, R. J Proulx, I. M Ross, L. C Wilcox

Ngôn ngữ: eng

Ký hiệu phân loại: 519.6 Mathematical optimization formerly 519.3

Thông tin xuất bản: 2019

Mô tả vật lý:

Bộ sưu tập: Metadata

ID: 162845

 Comment: 27 pages, 12 figures, JGCD April 2019Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points. Unfortunately, as $N$ increases, the condition number of the resulting linear algebra increases as $N^2$
  hence, spectral efficiency and accuracy are lost in practice. In this paper, we advance Birkhoff interpolation concepts over an arbitrary grid to generate well-conditioned PS optimal control discretizations. We show that the condition number increases only as $\sqrt{N}$ in general, but is independent of $N$ for the special case of one of the boundary points being fixed. Hence, spectral accuracy and efficiency are maintained as $N$ increases. The effectiveness of the resulting fast mesh refinement strategy is demonstrated by using \underline{polynomials of over a thousandth order} to solve a low-thrust, long-duration orbit transfer problem.
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