The shifts are obtained by means of a linear or nonlinear transformation while the Gaussian pseudospectral points are chosen from a collection of Gauss-Lobatto or Gauss-Radau distribution arising from Legendre or Chebyshev polynomials.
They can also be applied to infinite-horizon optimal control problems by a simple domain transformation technique.
In 2006, NASA used the Ross–Fahroo method to implement the "zero propellant maneuver" on board the International Space Station.
Ross was also elected AAS Fellow for "his pioneering contributions to pseudospectral optimal control."
That is, through a collection of theorems put forth by Ross and Fahroo,[5][6][8] [16] they showed that it was possible to design pseudospectral methods for optimal control that were equivalent in both the direct and indirect forms.