Integral constraint regularization method for fractional optimal control problem with pointwise state constraint

Abstract

This paper investigates integral constraint regularization approximation of fractional optimal control problem with pointwise state constraint. Firstly the continuous first-order optimality condition is derived. In order to deal with the irregular multiplier, a regularized optimal control problem with finitely many integral state constraints is proposed based on integral constraint regularization method. The error between the original solution and the regularized solution is deduced. Continuous piecewise linear finite element combined with variational discretization approach is used to discretize the regularized optimal control problem. Finite element discretization error combined with the regularization error leads to the final error estimate. Finally, numerical examples are presented to verify the theoretical findings.