OPTIMAL CONTROL OF A PARABOLIC DISTRIBUTED PARAMETER SYSTEM USING A FULLY EXPONENTIALLY CONVERGENT BARYCENTRIC SHIFTED GEGENBAUER INTEGRAL PSEUDOSPECTRAL METHOD

摘要

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