A Priori Error Estimates for Spectral Galerkin Approximations of Integral State-Constrained Fractional Optimal Control Problems  

作　　者：Juan Zhang Jiabin Song Huanzhen Chen 

机构地区：[1]School of Mathematics and Statistics,Linyi University,Linyi,Shandong 276000,China [2]School of Mathematics and Statistics,Shandong Normal University,Jinan,Shandong 250014,China [3]Department of Mathematics and Physics,Taishan College of Science and Technology,Taian,Shandong 271019,China

出　　处：《Advances in Applied Mathematics and Mechanics》2023年第3期568-582,共15页应用数学与力学进展（英文）

基　　金：This work was partly supported by National Natural Science Foundation of China(Grant Nos.:12101283,12271233 and 12171287);Natural Science Foundation of Shandong Province(Grant Nos.:ZR2019YQ05,2019KJI003,and ZR2016JL004).

摘　　要：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.

关 键 词：Fractional optimal control problem state constraint spectral method Jacobi polynomial a priori error estimate 

分 类 号：O17[理学—数学]