It is part of the larger theory of pseudospectral optimal control, a term coined by Ross.
Consequently, two different versions of the method have been proposed: one by Elnagar et al.,[2] and another by Fahroo and Ross.
In 2008, Trefethen showed that the Clenshaw–Curtis method was nearly as accurate as Gauss quadrature.
[4] This breakthrough result opened the door for a covector mapping theorem for Chebyshev PS methods.
[5] A complete mathematical theory for Chebyshev PS methods was finally developed in 2009 by Gong, Ross and Fahroo.