A Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control Problems (Advances in Applied Mathematics and Mechanics, 2023)
The fractional optimal control problem leads to significantly increased computational complexity compared to the corresponding classical integer-order optimalcontrol problem, due to the global properties of fractional differential operators. Inthis paper, we focus on an optimal control problem governed by fractional differentialequations with an integral constraint on the state variable. By the proposed first-orderoptimality condition consisting of a Lagrange multiplier, we design a spectral Galerkindiscrete 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 testsare given to demonstrate the validity and applicability of our proposed approximations and theoretical results.