  In this paper, we introduce a novel pseudospectral method for the numerical
solution of optimal control problems governed by a parabolic distributed
parameter system. The infinite-dimensional optimal control problem is reduced
into a finite-dimensional nonlinear programming problem through shifted
Gegenbauer quadratures constructed using a stable barycentric representation of
Lagrange interpolating polynomials and explicit barycentric weights for the
shifted Gegenbauer-Gauss (SGG) points. A rigorous error analysis of the method
is presented, and a numerical test example is given to show the accuracy and
efficiency of the proposed pseudospectral method.
