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Volume 15, Issue 6
Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian

Jiaqi Zhang, Yin Yang & Zhaojie Zhou

DOI: 10.4208/aamm.OA-2022-0173

Adv. Appl. Math. Mech., 15 (2023), pp. 1631-1654.

Published online: 2023-10

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35Q93, 49M25, 49M41

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-15-1631, author = {Zhang , JiaqiYang , Yin and Zhou , Zhaojie}, title = {Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2023}, volume = {15}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0173}, url = {http://global-sci.org/intro/article_detail/aamm/22054.html} }
TY - JOUR T1 - Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian AU - Zhang , Jiaqi AU - Yang , Yin AU - Zhou , Zhaojie JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1631 EP - 1654 PY - 2023 DA - 2023/10 SN - 15 DO - http://doi.org/10.4208/aamm.OA-2022-0173 UR - https://global-sci.org/intro/article_detail/aamm/22054.html KW - Fractional Laplacian, optimal control problem, Caffarelli-Silvestre extension, weighted Laguerre polynomials. AB -

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.

Jiaqi Zhang, Yin Yang & Zhaojie Zhou. (2023). Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian. Advances in Applied Mathematics and Mechanics. 15 (6). 1631-1654. doi:10.4208/aamm.OA-2022-0173
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