Mesh 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, 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 N in general, but it 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 polynomials of over one-thousandth order to solve a low-thrust long-duration orbit transfer problem.


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    Title :

    Fast Mesh Refinement in Pseudospectral Optimal Control


    Contributors:
    Koeppen, N. (author) / Ross, I. M. (author) / Wilcox, L. C. (author) / Proulx, R. J. (author)

    Published in:

    Publication date :

    2019-04-01




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English