research-article

A Hidden-Memory Variable-Order Time-Fractional Optimal Control Model: : Analysis and Approximation

Authors:

Xiangcheng Zheng,

Hong WangAuthors Info & Claims

SIAM Journal on Control and Optimization, Volume 59, Issue 3

Pages 1851 - 1880

https://doi.org/10.1137/20M1344962

Published: 01 January 2021 Publication History

Abstract

We prove the well-posedness and smoothing property of a fractional optimal control model with integral constraints governed by a hidden-memory variable-order Caputo time-fractional diffusion PDE, in which the adjoint equation leads to a different type of variable-order Riemann--Liouville time-fractional diffusion PDE. The L-1 discretization loses its monotonicity due to the impact of hidden memory, which was crucial in the error estimate of the L-1 discretization of constant-order fractional diffusion PDEs. We develop a novel splitting to prove an optimal-order error estimate of the discretization of the optimal control model without any artificial regularity assumption of the true solution. Numerical experiments are performed to substantiate the theoretical findings.

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Cited By

Fan WHu XZhu S(2023)Numerical Reconstruction of a Discontinuous Diffusive Coefficient in Variable-Order Time-Fractional SubdiffusionJournal of Scientific Computing10.1007/s10915-023-02237-y96:1Online publication date: 23-May-2023
https://dl.acm.org/doi/10.1007/s10915-023-02237-y
Jia JWang HZheng X(2022)Numerical Analysis of a Fast Finite Element Method for a Hidden-Memory Variable-Order Time-Fractional Diffusion EquationJournal of Scientific Computing10.1007/s10915-022-01820-z91:2Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s10915-022-01820-z
Zheng XWang H(2022)Discretization and Analysis of an Optimal Control of a Variable-Order Time-Fractional Diffusion Equation with Pointwise ConstraintsJournal of Scientific Computing10.1007/s10915-022-01795-x91:2Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s10915-022-01795-x
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cover image SIAM Journal on Control and Optimization

SIAM Journal on Control and Optimization Volume 59, Issue 3

DOI:10.1137/sjcodc.59.3

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© 2021, Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

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Published: 01 January 2021

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Cited By

Fan WHu XZhu S(2023)Numerical Reconstruction of a Discontinuous Diffusive Coefficient in Variable-Order Time-Fractional SubdiffusionJournal of Scientific Computing10.1007/s10915-023-02237-y96:1Online publication date: 23-May-2023
https://dl.acm.org/doi/10.1007/s10915-023-02237-y
Jia JWang HZheng X(2022)Numerical Analysis of a Fast Finite Element Method for a Hidden-Memory Variable-Order Time-Fractional Diffusion EquationJournal of Scientific Computing10.1007/s10915-022-01820-z91:2Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s10915-022-01820-z
Zheng XWang H(2022)Discretization and Analysis of an Optimal Control of a Variable-Order Time-Fractional Diffusion Equation with Pointwise ConstraintsJournal of Scientific Computing10.1007/s10915-022-01795-x91:2Online publication date: 1-May-2022
https://dl.acm.org/doi/10.1007/s10915-022-01795-x
Yang Z(2022)Numerical approximation and error analysis for Caputo–Hadamard fractional stochastic differential equationsZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-022-01890-x73:6Online publication date: 10-Nov-2022
https://dl.acm.org/doi/10.1007/s00033-022-01890-x
Guo YZheng X(2022)Analysis of viscoelastic flow with a generalized memory and its exponential convergence to steady stateZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-022-01688-x73:2Online publication date: 1-Apr-2022
https://dl.acm.org/doi/10.1007/s00033-022-01688-x
Yang ZZheng XWang H(2021)Well-posedness and regularity of Caputo–Hadamard fractional stochastic differential equationsZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-021-01566-y72:4Online publication date: 1-Aug-2021
https://dl.acm.org/doi/10.1007/s00033-021-01566-y

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