Optimal Control of a Parabolic Distributed Parameter System Using a Barycentric Shifted Gegenbauer Pseudospectral Method

Abstract

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.

15 pages, 3 figures

References in corpus (3)

• High-Order Numerical Solution of Second-Order One-Dimensional Hyperbolic Telegraph Equation Using a Shifted Gegenbauer Pseudospectral Method
• High-Order, Stable, And Efficient Pseudospectral Method Using Barycentric Gegenbauer Quadratures
• High-Order Adaptive Gegenbauer Integral Spectral Element Method for Solving Nonlinear Optimal Control Problems

Cited by in corpus (2)

• High-Order Shifted Gegenbauer Integral Pseudospectral Method for Solving Differential Equations of Lane-Emden Type
• A Direct Integral Pseudospectral Method for Solving a Class of Infinite-Horizon Optimal Control Problems Using Gegenbauer Polynomials and Certain Parametric Maps