The flat pseudospectral method is part of the family of the Ross–Fahroo pseudospectral methods introduced by Ross and Fahroo. The method combines the concept of differential flatness with pseudospectral method to generate outputs in the so-called flat space.
Concept
Because the differentiation matrix,
where
The combination of these concepts generates the flat pseudospectral method; that is, x and u are written as,
Thus, an optimal control problem can be quickly and easily transformed to a problem with just the Y pseudospectral variable.