Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian

Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian

Year:    2023

Author:    Jiaqi Zhang, Yin Yang, Zhaojie Zhou

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 6 : pp. 1631–1654

Abstract

In this paper spectral Galerkin approximation of optimal control problem governed by fractional elliptic equation is investigated. To deal with the nonlocality of fractional Laplacian operator the Caffarelli-Silvestre extension is utilized. The first order optimality condition of the extended optimal control problem is derived. A spectral Galerkin discrete scheme for the extended problem based on weighted Laguerre polynomials is developed. A priori error estimates for the spectral Galerkin discrete scheme is proved. Numerical experiments are presented to show the effectiveness of our methods and to verify the theoretical findings.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2022-0173

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 6 : pp. 1631–1654

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    24

Keywords:    Fractional Laplacian optimal control problem Caffarelli-Silvestre extension weighted Laguerre polynomials.

Author Details

Jiaqi Zhang

Yin Yang

Zhaojie Zhou