A Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control Problems
Year: 2023
Author: Juan Zhang, Jiabin Song, Huanzhen Chen
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 3 : pp. 568–582
Abstract
The fractional optimal control problem leads to significantly increased computational complexity compared to the corresponding classical integer-order optimal control problem, due to the global properties of fractional differential operators. In this paper, we focus on an optimal control problem governed by fractional differential equations with an integral constraint on the state variable. By the proposed first-order optimality condition consisting of a Lagrange multiplier, we design a spectral Galerkin discrete scheme with weighted orthogonal Jacobi polynomials to approximate the resulting state and adjoint state equations. Furthermore, a priori error estimates for state, adjoint state and control variables are discussed in details. Illustrative numerical tests are given to demonstrate the validity and applicability of our proposed approximations and theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0251
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 3 : pp. 568–582
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Fractional optimal control problem state constraint spectral method Jacobi polynomial a priori error estimate.
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