# Fast Mesh Refinement in Pseudospectral Optimal Control

arXiv: https://arxiv.org/abs/1904.12992 · HTML: https://mlsanity.com/paper/1904.12992/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Apr 2019.

## Built on by (most cited first, 1 of 1)

- [Advances in Trajectory Optimization for Space Vehicle Control](https://mlsanity.com/paper/2108.02335/) (2021)

## Abstract (arXiv)

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 N2; 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 √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 underlinepolynomials of over a thousandth order to solve a low-thrust, long-duration orbit transfer problem.