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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.

Zhang , JiaqiYang , Yin and Zhou , Zhaojie. (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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