  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, 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.
