Spectral Galerkin Approximation of Space Fractional Optimal Control Problem with Integral State Constraint

In this paper spectral Galerkin approximation of optimal control problem governed by fractional advection diffusion reaction equation with integral state constraint is investigated. First order optimal condition of the control problem is discussed. Weighted Jacobi polynomials are used to approximate...

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Bibliographic Details
Published inFractal and fractional Vol. 5; no. 3; p. 102
Main Authors Wang, Fangyuan, Li, Xiaodi, Zhou, Zhaojie
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 2021
Subjects
a priori error estimate
Approximation
Control theory
Estimates
Galerkin method
Integrals
Mathematical analysis
Optimal control
optimal control problem
Pollutants
Polynomials
spectral Galerkin method
state constraint
weighted Jacobi polynomials
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Summary:In this paper spectral Galerkin approximation of optimal control problem governed by fractional advection diffusion reaction equation with integral state constraint is investigated. First order optimal condition of the control problem is discussed. Weighted Jacobi polynomials are used to approximate the state and adjoint state. A priori error estimates for control, state, adjoint state and Lagrangian multiplier are derived. Numerical experiment is carried out to illustrate the theoretical findings.
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract5030102