Optimal control of a parabolic distributed parameter system using a fully exponentially convergent barycentric shifted Gegenbauer integral pseudospectral method

In this paper, we introduce a novel fully exponentially convergent direct integral pseudospectral method for the numerical solution of opti- mal control problems governed by a parabolic distributed parameter system. The proposed method combines the superior advantages possessed by the fam- ily of pseudospectral methods with the well-conditioning of integral operators through the use of the integral formulation of the distributed parameter sys- tem equations, and the spectral accuracy provided by the latest technology of Gegenbauer barycentric quadratures in a fashion that allows us to take advan- tage of the strengths of these three methodologies. 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 integral pseudospectral method.