TY - JOUR
T1 - A Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control Problems
AU - Zhang , Juan
AU - Song , Jiabin
AU - Chen , Huanzhen
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 568
EP - 582
PY - 2023
DA - 2023/02
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2021-0251
UR - https://global-sci.org/intro/article_detail/aamm/21441.html
KW - Fractional optimal control problem, state constraint, spectral method, Jacobi polynomial, a priori error estimate.
AB - <p style="text-align: justify;">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.</p>