Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/25669
Title: A space-time pseudospectral discretization method for solving diffusion optimal control problems with two-sided fractional derivatives
Author: Mushtaq Salh Ali
Mostafa Shamsi
Hassan Khosravian-Arab
Torres, Delfim F. M.
Farid Bozorgnia
Keywords: Optimal control of partial differential equations
Two-sided space–time fractional diffusion equations
Pseudospectral methods
Jacobi polynomials
Left and right differentiation matrices
Issue Date: 1-Mar-2019
Publisher: SAGE Publications
Abstract: We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is discretized by using the Jacobi–Gauss pseudospectral discretization and, in this way, the original problem is transformed into a classical integer–order optimal control problem. The main challenge, which we faced in this step, is to derive the left and right fractional differentiation matrices. In this respect, novel techniques for derivation of these matrices are presented. In the second step, the Legendre–Gauss–Radau pseudospectral method is employed. With these two steps, the original problem is converted into a convex quadratic optimization problem, which can be solved efficiently by available methods. Our approach can be easily implemented and extended to cover fractional optimal control problems with state constraints. Five test examples are provided to demonstrate the efficiency and validity of the presented method. The results show that our method reaches the solutions with good accuracy and a low central processing unit time.
Peer review: yes
URI: http://hdl.handle.net/10773/25669
DOI: 10.1177/1077546318811194
ISSN: 1077-5463
Publisher Version: http://dx.doi.org/10.1177/1077546318811194
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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